Dead-volume management in compressed-gas energy storage and recovery systems

ABSTRACT

In various embodiments, coupling losses between a cylinder assembly and other components of a gas compression and/or expansion system are reduced or eliminated via valve-timing control.

RELATED APPLICATIONS

This application claims the benefit of and priority to U.S. ProvisionalPatent Application No. 61/547,353, filed Oct. 14, 2011, U.S. ProvisionalPatent Application No. 61/569,528, filed Dec. 12, 2011, and U.S.Provisional Patent Application No. 61/620,018, filed Apr. 4, 2012. Theentire disclosure of each of these applications is hereby incorporatedherein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under DE-OE0000231awarded by the DOE. The government has certain rights in the invention.

FIELD OF THE INVENTION

In various embodiments, the present invention relates to pneumatics,hydraulics, power generation, and energy storage, and more particularly,to systems and methods using pneumatic, pneumatic/hydraulic, and/orhydraulic cylinders for energy storage and recovery.

BACKGROUND

Storing energy in the form of compressed gas has a long history andcomponents tend to be well tested and reliable, and have long lifetimes.The general principle of compressed-gas or compressed-air energy storage(CAES) is that generated energy (e.g., electric energy) is used tocompress gas (e.g., air), thus converting the original energy topressure potential energy; this potential energy is later recovered in auseful form (e.g., converted back to electricity) via gas expansioncoupled to an appropriate mechanism. Advantages of compressed-gas energystorage include low specific-energy costs, long lifetime, lowmaintenance, reasonable energy density, and good reliability.

If a body of gas is at the same temperature as its environment, andexpansion occurs slowly relative to the rate of heat exchange betweenthe gas and its environment, then the gas will remain at approximatelyconstant temperature as it expands. This process is termed “isothermal”expansion. Isothermal expansion of a quantity of high-pressure gasstored at a given temperature recovers approximately three times morework than would “adiabatic expansion,” that is, expansion where no heatis exchanged between the gas and its environment—e.g., because theexpansion happens rapidly or in an insulated chamber. Gas may also becompressed isothermally or adiabatically.

An ideally isothermal energy-storage cycle of compression, storage, andexpansion would have 100% thermodynamic efficiency. An ideally adiabaticenergy-storage cycle would also have 100% thermodynamic efficiency, butthere are many practical disadvantages to the adiabatic approach. Theseinclude the production of higher temperature and pressure extremeswithin the system, heat loss during the storage period, and inability toexploit environmental (e.g., cogenerative) heat sources and sinks duringexpansion and compression, respectively. In an isothermal system, thecost of adding a heat-exchange system is traded against resolving thedifficulties of the adiabatic approach. In either case, mechanicalenergy from expanding gas must usually be converted to electrical energybefore use.

An efficient and novel design for storing energy in the form ofcompressed gas utilizing near isothermal gas compression and expansionhas been shown and described in U.S. Pat. No. 7,832,207, filed Apr. 9,2009 (the '207 patent) and U.S. Pat. No. 7,874,155, filed Feb. 25, 2010(the '155 patent), the disclosures of which are hereby incorporatedherein by reference in their entireties. The '207 and '155 patentsdisclose systems and techniques for expanding gas isothermally in stagedcylinders and intensifiers over a large pressure range in order togenerate electrical energy when required. Mechanical energy from theexpanding gas may be used to drive a hydraulic pump/motor subsystem thatproduces electricity. Systems and techniques for hydraulic-pneumaticpressure intensification that may be employed in systems and methodssuch as those disclosed in the '207 and '155 patents are shown anddescribed in U.S. Pat. No. 8,037,678, filed Sep. 10, 2010 (the '678patent), the disclosure of which is hereby incorporated herein byreference in its entirety.

In the systems disclosed in the '207 and '155 patents, reciprocalmechanical motion is produced during recovery of energy from storage byexpansion of gas in the cylinders. This reciprocal motion may beconverted to electricity by a variety of techniques, for example asdisclosed in the '678 patent as well as in U.S. Pat. No. 8,117,842,filed Feb. 14, 2011 (the '842 patent), the disclosure of which is herebyincorporated herein by reference in its entirety. The ability of suchsystems to either store energy (i.e., use energy to compress gas into astorage reservoir) or produce energy (i.e., expand gas from a storagereservoir to release energy) will be apparent to any person reasonablyfamiliar with the principles of electrical and pneumatic machines.

In order to reduce overall pressure ranges of operation, various CAESsystems may utilize designs involving multiple interconnected cylinders.In such designs, trapped regions of “dead volume” may occur such thatpockets of gas remain in cylinders before and after valve transitions.Such volumes may occur within the cylinders themselves and/or withinconduits, valves, or other components within and interconnecting thecylinders. Bringing relatively high-pressure gas into communication(e.g., by the opening of a valve) with relatively low-pressure gaswithin a dead volume tends to lead to a diminishment of pressure of thehigher-pressure gas without the performance of useful work, therebydisadvantageously reducing the amount of work recoverable from or storedwithin the higher-pressure gas. Air dead volume tends to reduce theamount of work available from a quantity of high-pressure gas broughtinto communication with the dead volume. This loss of potential energymay be termed a “coupling loss.” For example, during a compression stagea volume of gas that was compressed to a relatively high pressure mayremain inside the compression cylinder, or conduits attached thereto,after the movable member of the cylinder (e.g., piston, hydraulic fluid,or bladder) reaches the end of its stroke. The volume of compressed airthat is not pushed onto the next stage at the end of stroke constitutes“dead volume” (also termed, in compressors, “clearance volume”). If thevolume of high-pressure gas within the cylinder is then brought intofluid communication (e.g., by the opening of a valve) with a section ofintake piping, a portion of the high-pressure gas will tend to enter thepiping and mix with the contents thereof, equalizing the pressure withinthe two volumes. This equalization of pressure entails a loss of exergy(i.e., energy available as work). In a preferred scenario, the gas inthe dead volume is allowed to expand in a manner that performs usefulwork (e.g., by pushing on a piston), equalizing in pressure with the gasin the piping prior to valve opening. In another scenario, the gas inthe dead volume is allowed to expand below the pressure of the gaswithin the intake piping, and pressure equalization takes place duringvalve transition (opening).

In another example of formation of dead space in a CAES system during anexpansion procedure, if gas is to be introduced into a cylinder througha valve for the purpose of performing work by pushing against a pistonwithin the cylinder, and a chamber or volume exists adjacent to thepiston that is filled with low-pressure gas at the time the valve isopened, the high-pressure gas entering the chamber is immediatelyreduced in pressure during free expansion and mixing with thelow-pressure gas and, therefore, performs less mechanical work upon thepiston than would have been possible without the pressure reduction. Thelow-pressure volume in such an example constitutes air dead volume. Deadvolume may also appear within the portion of a valve mechanism thatcommunicates with the cylinder interior, or within a tube or lineconnecting a valve to the cylinder interior, or within other componentsthat contain gas in various states of operation of the system. It willbe clear to persons familiar with hydraulics and pneumatics that deadvolume may also appear during compression procedures, and that energylosses due to pneumatically communicating dead volumes tend to beadditive.

Moreover, in an expander-compressor system operated to expand orcompress gas near-isothermally (i.e., at approximately constanttemperature) within a cylinder, gas that escapes the cylinder to becomedead volume (e.g., by displacing an incompressible fluid) in a hydraulicsubsystem may, as pressures change within the system, expand andcompress adiabatically (i.e., at non-constant temperature), withassociated energy losses due to heat transfer between the gas andmaterials surrounding the dead volume. These thermal energy losses willtend to be additive with losses that are due to non-work-performingexpansion of gas to lower pressures in dead volumes.

Therefore, in various compressor-expander systems, including isothermalcompressor-expander systems, preventing the formation of dead volumewill generally enable higher system efficiency. Attempts to minimizedead volume frequently involve reducing the sizes and lengths ofconduits interconnecting cylinders and other components. However, suchefforts may not eliminate all dead volume and tend to constrain theoverall geometry and placement of individual system components.Therefore, there is a need for alternative or additional approaches toreducing dead volume and/or the deleterious effects of dead volume inpneumatic components in order to reduce coupling losses and improveefficiency during compression and/or expansion of gas.

SUMMARY

Embodiments of the invention reduce the impact of dead volume inpneumatic cylinders and/or pneumatic chambers of pneumatic/hydrauliccylinders during compression and/or expansion in CAES systems. Theimpact of dead volume is reduced by time-coordinated matching of gaspressures within system components that would, absent such matching,suffer coupling losses and potential equipment damage. Herein, a spacewithin any component of a CAES system is termed a “dead volume” or “deadspace” if its volume cannot, in some or all states of operation, bereduced to zero due to mechanical constraints (e.g., imperfect fit of apiston to the interior face of a cylinder head when the piston is at topdead center, forming an ineradicable, residual chamber volume) and if insome states of system operation the space contains gas at a pressurethat can be brought into fluid communication with gas at a significantlydifferent pressure (e.g., through a valve transition).

In cylinders, the time-coordinated matching of pressures may beaccomplished using actuated valves that are selectively closed andopened in a manner that yields approximately matched pressures withinsystem components about to be brought into fluid communication with eachother. To reduce loss of exergy due to non-work-performing expansion ofgas when components containing gas at relatively high pressure (e.g.,3,000 psi) are brought into fluid communication with componentscontaining gas at relatively low pressure (e.g., 300 psi or atmosphericpressure), the gas in one or more potential dead spaces ispre-compressed to a pressure approximately equal to that of thehigher-pressure gas before the higher- and lower-pressure gas volumesare brought into fluid communication with each other. In otherembodiments, the gas in one or more potential dead spaces ispre-expanded to a pressure approximately equal to that of thelower-pressure gas before the higher- and lower-pressure volumes arebrought into fluid communication with each other. Such pre-compressionand pre-expansion produce specific target pressures (e.g., 3,000 psi) atspecific times or in specific states of system operation (e.g., when acylinder piston reaches top-dead-center position and is poised to beginan expansion stroke). Both target pressure and timing of pressurematching may be altered adaptively during the course of system operationbased on measurements of pressures within various parts of the CAESsystem and/or other aspects of system state. An actuated valve may beoperated (i.e., opened or closed) at specific times in order to reducethe effect of dead space, e.g., a valve may be opened only when apre-compression condition is met. The timing of actuated valve operationmay, furthermore, be conditioned on feedback in order to provideincreased system energy efficiency and/or other advantages. Herein, an“actuated” valve is a valve whose opening or closing occurs at a timethat may be altered, either arbitrarily or within limits, by a systemoperator or control mechanism, as distinct from a passive “check”-typevalve whose opening and closing are determined by differential pressuresor a “cam-driven” valve whose times of opening or closing are dictatedmechanically. Actuated valves may improve performance by opening attimes different than would be entailed by operation of check valves bydifferential pressures. Variable-timing cam-driven valves may beconsidered actuated valves and are within the scope of this invention.

In certain embodiments of the invention, the CAES system may include orconsist essentially of a cylinder assembly (or plurality of cylinderassemblies, e.g., multiple stages) that features a movable internalmember (e.g., piston) or other boundary mechanism such as hydraulicfluid or a bladder. The internal boundary mechanism of the cylinderdivides the interior of the cylinder into two chambers that may containdistinct bodies of fluid, and these may be at different pressures invarious states of operation of the system. The system may furtherinclude a first control valve in communication with a high-pressurestorage reservoir and the cylinder assembly, a second control valve incommunication with the cylinder assembly and a vent to atmosphere, aheat-transfer subsystem in fluid communication with the cylinderassembly, an electric motor/generator in mechanical communication with adrive mechanism (e.g., crankshaft, hydraulic pump, linear generatormover) configured to drive the movable member disposed within thecylinder assembly, and a control system configured to operate the firstand second control valves based on various information characterizingvarious aspects of the cylinder assembly and/or other components of thesystem (e.g., pressure, temperature, piston position, piston velocity).

One aspect of the invention relates to a method for reducing couplinglosses and improving system performance during an expansion stage of aCAES system. In various embodiments, gas within a first chamber of acylinder is pressurized to approximately some relatively high pressure(e.g., 3,000 psi) at or near the beginning of an expansion stroke of thecylinder. In this state of operation, the piston of the cylinder is ator near its top dead center position and the first chamber constitutesdead volume. A first control valve is then operated to place a volume ofhigh-pressure gas (e.g., air at 3,000 psi) from an external source(e.g., a pressurized gas storage reservoir) in fluid communication withthe first chamber. Because the gas within the first chamber is atapproximately the same pressure as the high-pressure source placed incommunication with the first chamber by the opening of the first controlvalve, gas from the high-pressure source does not tend to expand intothe first chamber suddenly and without performing useful work. Couplinglosses during the connection of the source to the cylinder are thusreduced or eliminated. In short, system performance may be improved byforestalling events of rapid pressure equalization of connecting spaces.

During a subsequent cylinder expansion stroke (also herein termed a“downward stroke”), useful work is recovered from high-pressure gasduring both (1) admission of high-pressure gas to the first cylinderchamber while the boundary mechanism moves downward so as to allow thefirst cylinder chamber to enlarge, a phase of operation herein termed a“direct-drive phase” or “direct drive,” and (2) a subsequent expansionphase (i.e., after the first control valve is closed) during which theboundary mechanism continues to move downward and a fixed mass ofhigh-pressure gas expands in the enlarging first chamber). As shown anddescribed in the '207 and '155 patents and the '128 application, gasexpansion may be maintained as substantially isothermal by introducing acertain volume of liquid (e.g., a quantity of foam or spray) at anappropriate temperature into the cylinder prior to and/or during theexpansion.

At or near the end of the expansion stroke, when the gas reaches a lowerpressure (e.g., 300 psi), a second control valve is operated to begin toexhaust the gas (e.g., to a vent and/or to a mid-pressure vessel andsecond cylinder assembly) as an upward stroke of the movable memberwithin the piston occurs. During the first portion of the second half ofthe cylinder stroke (e.g., the upward stroke), the gas is exhaustedthrough the second control valve (e.g., into a mid-pressure vessel andsecond cylinder assembly) by translating the movable member (e.g.,piston) or other boundary mechanism to reduce the volume of the firstchamber in the cylinder assembly. During a second portion of the secondhalf of the cylinder stroke (e.g., the upward stroke), prior to themovable member reaching the end of stroke (e.g., top of stroke) insidethe cylinder, the second control valve is closed and a “pre-compressionstroke” is performed to compress the remaining volume of air (deadvolume) and/or liquid inside the cylinder.

The time of closure of the second control valve, relative to thesequence of states of operation just described, is not arbitrary.Premature closure of the second valve will typically tend to trap anexcessive quantity of gas in the first chamber, resulting inoverpressurization of the gas in the first chamber when the volume ofthe first chamber attains a minimum (i.e., at top dead center ofstroke). When this occurs, opening of the first valve at the start ofthe next expansion cycle will result in energy loss throughnon-work-performing expansion of the gas within the first chamber intothe high-pressure storage reservoir and other components (e.g., piping)in fluid communication therewith.

On the other hand, tardy closure of the second valve will tend to trapan inadequate quantity of gas in the first chamber, resulting inunderpressurization of the gas in the first chamber when the volume ofthe first chamber attains a minimum (i.e., at top dead center ofstroke). When this occurs, opening of the first valve at the start ofthe next expansion cycle will generally result in energy loss throughnon-work-performing expansion of gas from the high-pressure storagereservoir and other components (e.g., piping) in fluid communicationtherewith into the first chamber.

Therefore, in certain embodiments of the invention the optimal time ofactuation of the second control valve is based at least in part onsensed conditions in one or more portions of the CAES system, e.g.,pressure in the first chamber, pressure in the high-pressure storagereservoir, piston position, piston velocity, etc. The principles onwhich the time of actuation of the second control valve is determinedwill be made clear hereinbelow.

When liquid is introduced into the first chamber to enable approximatelyisothermal expansion, a quantity of liquid will generally accumulate inthe first chamber (e.g., on top of the piston or other movable member)during an expansion stroke. In an ideal case, i.e., if all of the gascompressed in the first chamber is passed to the storage reservoir or toa higher-pressure cylinder stage by the time the volume of the firstchamber is at a minimum, the remaining volume of the first chamber(i.e., the volume between the movable member and the interior face ofthe upper end-cap of the cylinder) will be occupied entirely by liquid;all gas will have been expelled and there will be no gas-filled deadvolume in the first chamber at the commencement of a new expansionstroke. However, in practice, the first chamber volume at thecommencement of a new expansion stroke will tend to contain both liquidand gas remaining from the previous expansion stroke. The gas fractionof this volume may constitute dead volume at the start of the newstroke. During the pre-compression stroke, therefore, as alreadydescribed hereinabove, the effective coupling loss due to this deadvolume is minimized by compressing the remaining air to a pressuresubstantially equal to the pressure of the air in the storage reservoir(or the pressure of the gas to be introduced into the cylinder forexpansion, if such gas is not arriving directly from the storagereservoir). Thus, when additional high-pressure gas is admitted to thecylinder for expansion, no or minimal pressure difference exists betweenthe two sides of the first control valve. This allows the first controlvalve to be operated with a lower actuation energy, further improvingsystem efficiency.

Most or even substantially all of the work done upon the air in thefirst chamber during a pre-compression stroke is typically recovered asthe air re-expands during the subsequent expansion stroke. Furthermore,if the pressure of the air in the dead volume is approximately equal tothe pressure of the air in the storage vessel or the nexthigher-pressure stage, then there will be substantially no coupling losswhen the first valve to the storage reservoir or next-higher-pressurestage is opened. The higher pressure within the dead volume entails lessgas flow from the storage reservoir or next-higher-pressure stage to thecylinder when the valve is opened during an expansion stage, therebyreducing coupling loss and improving efficiency. Moreover, the longevityof some system components may be increased because transient mechanicalstresses caused by high-pressure air rushing suddenly into dead volumeare minimized or eliminated.

Employing measurements of pressures within various components (e.g.,lines and chambers) allows the timing of actuated-valve closings andopenings (i.e., valve transition events) to be optimized for specificsystem conditions. For example, CAES systems constructed according tosimilar designs may differ in pipe lengths and other details affectingpotential dead space. In such a case, with actuated valves, valvetransition events may be tuned to optimize efficiency of an individualsystem by minimizing dead-space coupling losses. For example, if anoverpressure is detected in a pre-pressurized cylinder chamber, closureof the valve that permits gas to exit the chamber during a return strokemay be retarded to reduce the amount of pre-pressurized gas. A CAESsystem in which valve transition event tuning is performed by acomputerized system controller may be considered, in this respect, aself-tuning system. For another example, as the pressure within a gasstorage reservoir declines as the gas within the reservoir cools or isexhausted (or increases as the gas within the reservoir warms or isaugmented), valve transition event timing may be tuned in a manner thatadaptively, continuously maximizes the energy efficiency of the CAESsystem. Thus, a CAES system in accordance with various embodiments ofthe invention may adaptively self-tune its valve transition events so asto minimize dead-space coupling losses in response both toidiosyncrasies of system construction and to changing conditions ofoperation.

Furthermore, to minimize the impacts of dead space, the timing of valveactuations may be chosen in light of the non-ideal features of actualvalves. Non-instantaneous valve transitions tend to entail tradeoffsbetween system capacity (amount of air compressed or expanded perstroke) and system efficiency (partly determined by energy losses due todead space). The impact of non-ideal valve actuation on CAES systemoperation is considered for certain embodiments of the inventionhereinbelow.

Every compression or expansion of a quantity of gas, where such acompression or expansion is herein termed “a gas process,” is generallyone of three types: (1) adiabatic, during which the gas exchanges noheat with its environment and, consequently, rises or falls intemperature, (2) isothermal, during which the gas exchanges heat withits environment in such a way as to remain at constant temperature, and(3) polytropic, during which the gas exchanges heat with its environmentbut its temperature does not remain constant. Perfectly adiabatic gasprocesses are not practical because some heat is always exchangedbetween any body of gas and its environment (ideal insulators andreflectors do not exist); perfectly isothermal gas processes are notpractical because for heat to flow between a quantity of gas and aportion of its environment (e.g., a body of liquid), a nonzerotemperature difference must exist between the gas and itsenvironment—e.g., the gas must be allowed to heat during compression inorder that heat may be conducted to the liquid. Hence real-world gasprocesses are typically polytropic, though they may approximateadiabatic or isothermal processes.

The Ideal Gas Law states that for a given quantity of gas having mass m,pressure p, volume V, and temperature T, pV=mRT, where R is the gasconstant (R=287 J/K·kg for air). For an isothermal process, T is aconstant throughout the process, so pV=C, where C is some constant.

For a polytropic process, as will be clear to persons familiar with thescience of thermodynamics, pV^(n)=C throughout the process, where n,termed the polytropic index, is some constant generally between 1.0 and1.6. For n=1, pV^(n)=pV¹=pV=C, i.e., the process is isothermal. Ingeneral, a process for which n is close to 1 (e.g., 1.05) may be deemedapproximately isothermal.

For an adiabatic process, pV^(i)=C, where γ, termed the adiabaticcoefficient, is equal to the ratio of the gas's heat capacity atconstant pressure C_(P) to its heat capacity at constant volume, C_(V),i.e., γ=C_(P)/C_(V). In practice, γ is dependent on pressure. For air,the adiabatic coefficient γ is typically between 1.4 and 1.6.

Herein, we define a “substantially isothermal” gas process as one havingn≦1.1. The gas processes conducted within cylinders described herein arepreferably substantially isothermal with n≦1.05. Herein, wherever a gasprocess taking place within a cylinder assembly or storage reservoir isdescribed as “isothermal,” this word is synonymous with the term“substantially isothermal.”

The amount of work done in compression or expansion of a given quantityof gas varies substantially with polytropic index n. For compressions,the lowest amount of work done is for an isothermal process and thehighest for an adiabatic process, and vice versa for expansions. Hence,for gas processes such as typically occur in the compressed-gas energystorage systems described herein, the end temperatures attained byadiabatic, isothermal, and substantially isothermal gas processes aresufficiently different to have practical impact on the operability andefficiency of such systems. Similarly, the thermal efficiencies ofadiabatic, isothermal, and substantially isothermal gas processes aresufficiently different to have practical impact on the overallefficiency of such energy storage systems. For example, for compressionof a quantity of gas from initial temperature of 20° C. and initialpressure of 0 psig (atmospheric) to a final pressure of 180 psig, thefinal temperature T of the gas will be exactly 20° C. for an isothermalprocess, approximately 295° C. for an adiabatic process, approximately95° C. for a polytropic compression having polytropic index n=1.1 (10%increase in n over isothermal case of n=1), and approximately 60° C. fora polytropic compression having polytropic index n=1.05 (5% increase inn over isothermal case of n=1). In another example, for compression of1.6 kg of air from an initial temperature of 20° C. and initial pressureof 0 psig (atmospheric) to a final pressure of approximately 180 psig,including compressing the gas into a storage reservoir at 180 psig,isothermal compression requires approximately 355 kilojoules of work,adiabatic compression requires approximately 520 kilojoules of work, anda polytropic compression having polytropic index n=1.045 requiresapproximately 375 kilojoules of work; that is, the polytropiccompression requires approximately 5% more work than the isothermalprocess, and the adiabatic process requires approximately 46% more workthan the isothermal process.

It is possible to estimate the polytropic index n of gas processesoccurring in cylinder assemblies such as are described herein byempirically fitting n to the equation pV^(n)=C, where pressure p andvolume V of gas during a compression or expansion, e.g., within acylinder, may both be measured as functions of time from pistonposition, known device dimensions, and pressure-transducer measurements.Moreover, by the Ideal Gas Law, temperature within the cylinder may beestimated from p and V, as an alternative to direct measurement by atransducer (e.g., thermocouple, resistance thermal detector, thermistor)located within the cylinder and in contact with its fluid contents. Inmany cases, an indirect measurement of temperature via volume andpressure may be more rapid and more representative of the entire volumethan a slower point measurement from a temperature transducer. Thus,temperature measurements and monitoring described herein may beperformed directly via one or more transducers, or indirectly asdescribed above, and a “temperature sensor” may be one of such one ormore transducers and/or one or more sensors for the indirect measurementof temperature, e.g., volume, pressure, and/or piston-position sensors.

All of the approaches described above for converting potential energy ina compressed gas into mechanical and electrical energy may, ifappropriately designed, be operated in reverse to store electricalenergy as potential energy in a compressed gas. Since the accuracy ofthis statement will be apparent to any person reasonably familiar withthe principles of electrical machines, power electronics, pneumatics,and the principles of thermodynamics, the operation of these mechanismsto both store energy and recover it from storage are not necessarilydescribed for each embodiment. Such operation is, however, contemplatedand within the scope of the invention and may be straightforwardlyrealized without undue experimentation.

The systems described herein, and/or other embodiments employingfoam-based heat exchange, liquid-spray heat exchange, and/or externalgas heat exchange, may draw or deliver thermal energy via theirheat-exchange mechanisms to external systems (not shown) for purposes ofcogeneration, as described in U.S. Pat. No. 7,958,731, filed Jan. 20,2010 (the '731 patent), the entire disclosure of which is incorporatedby reference herein.

The compressed-air energy storage and recovery systems described hereinare preferably “open-air” systems, i.e., systems that take in air fromthe ambient atmosphere for compression and vent air back to the ambientatmosphere after expansion, rather than systems that compress and expanda captured volume of gas in a sealed container (i.e., “closed-air”systems). The systems described herein generally feature one or morecylinder assemblies for the storage and recovery of energy viacompression and expansion of gas. The systems also include (i) areservoir for storage of compressed gas after compression and supply ofcompressed gas for expansion thereof, and (ii) a vent for exhaustingexpanded gas to atmosphere after expansion and supply of gas forcompression. The storage reservoir may include or consist essentiallyof, e.g., one or more one or more pressure vessels (i.e., containers forcompressed gas that may have rigid exteriors or may be inflatable, thatmay be formed of various suitable materials such as metal or plastic,and that may or may not fall within ASME regulations for pressurevessels), pipes (i.e., rigid containers for compressed gas that may alsofunction as and/or be rated as fluid conduits, have lengths well inexcess (e.g., >100×) of their diameters, and do not fall within ASMEregulations for pressure vessels), or caverns (i.e., naturally occurringor artificially created cavities that are typically locatedunderground). Open-air systems typically provide superior energy densityrelative to closed-air systems.

Furthermore, the systems described herein may be advantageously utilizedto harness and recover sources of renewable energy, e.g., wind and solarenergy. For example, energy stored during compression of the gas mayoriginate from an intermittent renewable energy source of, e.g., wind orsolar energy, and energy may be recovered via expansion of the gas whenthe intermittent renewable energy source is nonfunctional (i.e., eithernot producing harnessable energy or producing energy atlower-than-nominal levels). As such, the systems described herein may beconnected to, e.g., solar panels or wind turbines, in order to store therenewable energy generated by such systems.

In one aspect, embodiments of the invention feature a method ofincreasing efficiency of an energy-recovery process performed in acylinder assembly in which gas is expanded from an initial pressure to afinal pressure. Gas is pre-compressed in the cylinder assembly toapproximately the initial pressure, and, following pre-compression,compressed gas is admitted at the initial pressure into the cylinderassembly. The pre-compression reduces coupling loss during the admissionof compressed gas. Gas is expanded in the cylinder assembly to the finalpressure, and the expansion cycle is completed by exhausting only aportion of the expanded gas out of the cylinder assembly. The foregoingsteps may be repeated at least once, thereby performing at least oneadditional expansion cycle.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. The gas may be thermally conditionedwith heat-transfer fluid during expansion. The thermal conditioning mayrender the expansion substantially isothermal. The heat-transfer fluidmay be sprayed into the gas and/or may form a foam with the gas. Afterexpansion of the gas, at least a portion of the heat-transfer fluid maybe exhausted out of the cylinder assembly. The compressed gas may beadmitted into the cylinder assembly from a storage reservoir containinggas at the initial pressure. The compressed gas may be admitted into thecylinder assembly from a second cylinder assembly in which gas isexpanded to the initial pressure from a pressure greater than theinitial pressure. The portion of the expanded gas may be exhausted tothe ambient atmosphere or to a second cylinder assembly in which gas isexpanded from the final pressure to a pressure lower than the finalpressure. Admitting compressed gas into the cylinder assembly mayinclude or consist essentially of actuating a valve to establish aconnection between the cylinder assembly and a source of the compressedgas. The pre-compression may reduce the actuation energy required toactuate the valve. At least a portion of the gas that is pre-compressedmay be within dead volume of the cylinder assembly. Exhausting only aportion of the expanded gas out of the cylinder assembly may include orconsist essentially of exhausting substantially all of the expanded gasin the cylinder assembly that is not within dead volume of the cylinderassembly. The amount of the gas that is pre-compressed may besubstantially less than an amount of the gas expanded in the cylinderassembly.

A temperature, a pressure, and/or a position of a boundary mechanismwithin the cylinder assembly may be monitored during gas expansionand/or gas exhaustion, thereby generating control information. Thecontrol information may be utilized in a subsequent expansion cycle tocontrol at least one of the pre-compression, expansion, or exhaustionsteps. The gas expansion may drive a load connected to the cylinderassembly, e.g., a mechanical crankshaft or a hydraulic pump/motor. Thegas expansion may generate electricity. Exhausting only a portion of theexpanded gas out of the cylinder assembly may include or consistessentially of (i) monitoring a temperature, a pressure, and/or aposition of a boundary mechanism within the cylinder assembly, therebygenerating control information, and (ii) based at least in part on thecontrol information, discontinuing the gas exhaustion, thereby trappinga remnant portion of the expanded gas within the cylinder assembly. Theremnant portion of the expanded gas may be determined such that apre-compression step of a subsequent expansion cycle compresses theremnant portion to approximately the initial pressure.

In another aspect, embodiments of the invention feature a method ofincreasing efficiency of an energy-storage process performed in acylinder assembly in which gas is compressed from an initial pressure toa final pressure. Gas is pre-expanded in the cylinder assembly toapproximately the initial pressure. Following the pre-expansion, gas isadmitted at the initial pressure into the cylinder assembly. Thepre-expansion reduces coupling loss during the admission of gas. (Duringpre-expansion, work is being recovered via the expansion of the gas,e.g., via movement of a piston or other boundary mechanism, and valvesto the cylinder assembly are closed, in contrast to a case, e.g., wheregas expands and is free to exhaust from the cylinder assembly toatmosphere, and no work is recovered therefrom.) The gas is compressedin the cylinder assembly to the final pressure, and a compression cycleis completed by exhausting only a portion of the compressed gas out ofthe cylinder assembly. The foregoing steps may be repeated at leastonce, thereby performing at least one additional compression cycle.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. The gas may be thermally conditionedwith heat-transfer fluid during compression. The thermal conditioningmay render the compression substantially isothermal. The heat-transferfluid may be sprayed into the gas and/or form a foam with the gas. Aftercompression of the gas, at least a portion of the heat-transfer fluidmay be exhausted out of the cylinder assembly. The gas may be admittedinto the cylinder assembly from a vent to atmosphere, and the initialpressure may be approximately atmospheric pressure. The gas may beadmitted into the cylinder assembly from a second cylinder assembly inwhich gas is compressed to the initial pressure from a pressure lessthan the initial pressure. The portion of the compressed gas may beexhausted to a compressed-gas storage reservoir. The portion of theexpanded gas may be exhausted to a second cylinder assembly in which gasis compressed from the final pressure to a pressure higher than thefinal pressure. Admitting gas into the cylinder assembly may include orconsist essentially of actuating a valve to establish a connectionbetween the cylinder assembly and a source of the gas. The pre-expansionmay reduce the actuation energy required to actuate the valve. At leasta portion of the gas that is pre-expanded may be within dead volume ofthe cylinder assembly. Exhausting only a portion of the compressed gasout of the cylinder assembly may include or consist essentially ofexhausting substantially all of the compressed gas in the cylinderassembly that is not within dead volume of the cylinder assembly. Theamount of the gas that is pre-expanded may be substantially less than anamount of the gas compressed in the cylinder assembly.

A temperature, a pressure, and/or a position of a boundary mechanismwithin the cylinder assembly may be monitored during gas compressionand/or gas exhaustion, thereby generating control information. Thecontrol information may be utilized in a subsequent compression cycle tocontrol at least one of the pre-expansion, compression, or exhaustionsteps. The gas compression may be driven by a load connected to thecylinder assembly, e.g., a mechanical crankshaft or a hydraulicpump/motor. Exhausting only a portion of the compressed gas out of thecylinder assembly may include or consist essentially of (i) monitoring atemperature, a pressure, and/or a position of a boundary mechanismwithin the cylinder assembly, thereby generating control information,and (ii) based at least in part on the control information,discontinuing the gas exhaustion, thereby trapping a remnant portion ofthe compressed gas within the cylinder assembly. The remnant portion ofthe compressed gas may be determined such that a pre-expansion step of asubsequent expansion cycle expands the remnant portion to approximatelythe initial pressure.

In yet another aspect, embodiments of the invention feature an energystorage and recovery system that includes or consists essentially of acylinder assembly for expanding gas to recover energy and/or compressinggas to store energy, a high-side component selectively fluidly connectedto the cylinder assembly, a low-side component selectively fluidlyconnected to the cylinder assembly, and a control system. The high-sidecomponent supplies gas to the cylinder assembly for expansion thereinand/or accepts gas from the cylinder assembly after compression therein.The low-side component supplies gas to the cylinder assembly forcompression therein and/or accepts gas from the cylinder assembly afterexpansion therein. The control system operates the cylinder assembly toperform (i) a pre-compression of gas therewithin prior to admissiontherein of gas for expansion, thereby reducing coupling loss between thecylinder assembly and the high-side component, and/or (ii) apre-expansion of gas therewithin prior to admission therein of gas forcompression, thereby reducing coupling loss between the cylinderassembly and the low-side component.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. A sensor may sense a temperature, apressure, or a position of a boundary mechanism within the cylinderassembly to generate control information, and the control system may beresponsive to the control information. The control system may beconfigured to operate the cylinder assembly, during (i) pre-compressionof gas therewithin and/or (ii) expansion of gas therewithin, based atleast in part on control information generated during (i) a previous gasexpansion within the cylinder assembly and/or (ii) a previouspre-compression of gas within the cylinder assembly. The control systemmay be configured to operate the cylinder assembly, during (i)pre-expansion of gas therewithin and/or (ii) compression of gastherewithin, based at least in part on control information generatedduring (i) a previous gas compression within the cylinder assemblyand/or (ii) a previous pre-expansion of gas within the cylinderassembly. The high-side component may include or consist essentially ofa compressed-gas storage reservoir. The high-side component may includeor consist essentially of a second cylinder assembly for compressing gasand/or expanding gas within a pressure range higher than a pressurerange of operation of the cylinder assembly. The system may include asecond cylinder assembly for compressing gas and/or expanding gas withina pressure range higher than a pressure range of operation of thecylinder assembly, and the high-side component may include or consistessentially of a mid-pressure vessel for containing gas at a pressurewithin both of or between pressure ranges of operation of the cylinderassembly and the second cylinder assembly. The low-side component mayinclude or consist essentially of a vent to atmosphere. The low-sidecomponent may include or consist essentially of a second cylinderassembly for compressing gas and/or expanding gas within a pressurerange lower than a pressure range of operation of the cylinder assembly.The system may include a second cylinder assembly for compressing gasand/or expanding gas within a pressure range lower than a pressure rangeof operation of the cylinder assembly, and the low-side component mayinclude or consist essentially of a mid-pressure vessel for containinggas at a pressure within both of or between pressure ranges of operationof the cylinder assembly and the second cylinder assembly.

A load may be mechanically coupled to the cylinder assembly. The loadmay be driven by the cylinder assembly during gas expansion and/or drivethe cylinder assembly during gas compression. The load may include orconsist essentially of at least one of a mechanical crankshaft or ahydraulic pump/motor. The system may include a heat-transfer subsystemfor thermally conditioning gas during compression and/or expansionthereof. The heat-transfer subsystem may include or consist essentiallyof a mechanism for introducing heat-transfer fluid into the gas, e.g., aspray head and/or a spray rod. The heat-transfer subsystem may include aheat exchanger for thermally conditioning gas from the cylinder assemblyand/or heat-transfer fluid. The heat-transfer subsystem may include (i)a mixing chamber for forming foam from gas and heat-transfer fluidand/or (ii) a screen for altering average bubble size and/or bubble-sizevariance of foam comprising gas and heat-transfer fluid.

In a further aspect, embodiments of the invention feature a method ofincreasing efficiency of an energy-recovery process performed in acylinder assembly in which gas is expanded. The cylinder assembly isselectively fluidly connected to a high-side component by a high-sidevalve and selectively fluidly connected to a low-side component by alow-side valve. A first valve transition is performed by opening thehigh-side valve to allow compressed gas to enter the cylinder assemblyfrom the high-side component, and the cylinder assembly contains gas ata first pressure prior to the first valve transition. A second valvetransition is performed by closing the high-side valve, and the gaswithin the cylinder assembly expands thereafter. A third valvetransition is performed by opening the low-side valve to allow a portionof the expanded gas to enter the low-side component from the cylinderassembly, and (i) a remnant portion of the gas remains in the cylinderassembly after the third valve transition and (ii) the expanded gas isat a second pressure prior to the third valve transition. A fourth valvetransition is performed by closing the low-side valve, and the remnantportion of the gas within the cylinder assembly is compressed thereafterto approximately the first pressure. A transition restriction isenforced, where the transition restriction includes or consistsessentially of (i) performing the first valve transition only when thefirst pressure is approximately equal to a pressure of the high-sidecomponent and/or (ii) performing the third valve transition only whenthe second pressure is approximately equal to a pressure of the low-sidecomponent.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. The high-side component may include orconsist essentially of a compressed-gas storage reservoir. The high-sidecomponent may include or consist essentially of a second cylinderassembly for compressing gas and/or expanding gas within a pressurerange higher than a pressure range of operation of the cylinderassembly. The high-side component may include or consist essentially ofa mid-pressure vessel for containing gas at a pressure within both of orbetween pressure ranges of operation of the cylinder assembly and asecond cylinder assembly for compressing gas and/or expanding gas withina pressure range higher than a pressure range of operation of thecylinder assembly. The low-side component may include or consistessentially of a vent to atmosphere. The low-side component may includeor consist essentially of a second cylinder assembly for compressing gasand/or expanding gas within a pressure range lower than a pressure rangeof operation of the cylinder assembly. The low-side component mayinclude or consist essentially of a mid-pressure vessel for containinggas at a pressure within both of or between pressure ranges of operationof the cylinder assembly and a second cylinder assembly for compressinggas and/or expanding gas within a pressure range lower than a pressurerange of operation of the cylinder assembly.

The high-side valve and/or the low-side valve may be actuated valves.Each of the high-side valve and the low-side valve may be ahydraulically actuated valve, a variable cam actuated valve, anelectromagnetically actuated valve, a mechanically actuated valve, or apneumatically actuated valve. The second valve transition may be timedto admit an amount of gas into a volume of the cylinder assembly that isexpandable to the second pressure in the cylinder assembly. Atemperature within the cylinder assembly, a pressure within the cylinderassembly, a position of a boundary mechanism within the cylinderassembly, the pressure of the high-side component, and/or the pressureof the low-side component may be monitored during an expansion cycleincluding or consisting essentially of the first, second, third, andfourth valve transitions, thereby generating control information. Thecontrol information may be utilized in a subsequent expansion cycle tocontrol timing of the first, second, third, and/or fourth valvetransitions of the subsequent expansion cycle. The timing may becontrolled to maximize efficiency of the subsequent expansion cycle. Gasmay be thermally conditioned with heat-transfer fluid during at least aportion of an expansion cycle including or consisting essentially of thefirst, second, third, and fourth valve transitions. The thermalconditioning may render the gas expansion substantially isothermal.

In yet a further aspect, embodiments of the invention feature a methodof increasing efficiency of an energy-recovery process performed in acylinder assembly in which gas is expanded. The cylinder assembly isselectively fluidly connected to a high-side component by a high-sidevalve and selectively fluidly connected to a low-side component by alow-side valve. A plurality of expansion cycles are performed within thecylinder assembly. Each expansion cycle includes or consists essentiallyof (i) performing a first valve transition by opening the high-sidevalve to allow compressed gas to enter the cylinder assembly from thehigh-side component, (ii) performing a second valve transition byclosing the high-side valve, the gas within the cylinder assemblyexpanding thereafter, (iii) performing a third valve transition byopening the low-side valve to allow a portion of the expanded gas toenter the low-side component from the cylinder assembly, a remnantportion of the gas remaining in the cylinder assembly after the thirdvalve transition, and (iv) performing a fourth valve transition byclosing the low-side valve, the remnant portion of the gas within thecylinder assembly being compressed thereafter. During each expansioncycle, the timing of the first, second, third, and/or fourth valvetransitions is altered to maximize efficiency of the expansion cycle.The timing may be altered based at least in part on control informationgenerated during a previous expansion cycle. The control information mayinclude or consist essentially of a temperature within the cylinderassembly, a pressure within the cylinder assembly, a position of aboundary mechanism within the cylinder assembly, the pressure of thehigh-side component, and/or the pressure of the low-side component.

In another aspect, embodiments of the invention feature a method ofincreasing efficiency of an energy-storage process performed in acylinder assembly in which gas is compressed. The cylinder assembly isselectively fluidly connected to a high-side component by a high-sidevalve and selectively fluidly connected to a low-side component by alow-side valve. A first valve transition is performed by opening thelow-side valve to allow gas to enter the cylinder assembly from thelow-side component, and the cylinder assembly contains gas at a firstpressure prior to the first valve transition. A second valve transitionis performed by closing the low-side valve, and the gas within thecylinder assembly is compressed thereafter. A third valve transition isperformed by opening the high-side valve to allow a portion of thecompressed gas to enter the high-side component from the cylinderassembly, and (i) a remnant portion of the gas remains in the cylinderassembly after the third valve transition and (ii) the compressed gas isat a second pressure prior to the third valve transition. A fourth valvetransition is performed by closing the high-side valve, and the remnantportion of the gas within the cylinder assembly expands thereafter toapproximately the first pressure. A transition restriction is enforced,where the transition restriction includes or consists essentially of (i)performing the first valve transition only when the first pressure isapproximately equal to a pressure of the low-side component or (ii)performing the third valve transition only when the second pressure isapproximately equal to a pressure of the high-side component.

Embodiments of the invention may include one or more of the following inany of a variety of combinations. The high-side component may include orconsist essentially of a compressed-gas storage reservoir. The high-sidecomponent may include or consist essentially of a second cylinderassembly for compressing gas and/or expanding gas within a pressurerange higher than a pressure range of operation of the cylinderassembly. The high-side component may include or consist essentially ofa mid-pressure vessel for containing gas at a pressure within both of orbetween pressure ranges of operation of the cylinder assembly and asecond cylinder assembly for compressing gas and/or expanding gas withina pressure range higher than a pressure range of operation of thecylinder assembly. The low-side component may include or consistessentially of a vent to atmosphere. The low-side component may includeor consist essentially of a second cylinder assembly for compressing gasand/or expanding gas within a pressure range lower than a pressure rangeof operation of the cylinder assembly. The low-side component mayinclude or consist essentially of a mid-pressure vessel for containinggas at a pressure within both of or between pressure ranges of operationof the cylinder assembly and a second cylinder assembly for compressinggas and/or expanding gas within a pressure range lower than a pressurerange of operation of the cylinder assembly.

The high-side valve and/or the low-side valve may be actuated valves.Each of the high-side valve and the low-side valve may be ahydraulically actuated valve, a variable cam actuated valve, anelectromagnetically actuated valve, a mechanically actuated valve, or apneumatically actuated valve. The second valve transition may be timedto admit an amount of gas into a volume of the cylinder assembly that iscompressible to the second pressure in the cylinder assembly. Atemperature within the cylinder assembly, a pressure within the cylinderassembly, a position of a boundary mechanism within the cylinderassembly, the pressure of the high-side component, and/or the pressureof the low-side component may be monitored during a compression cycleincluding or consisting essentially of the first, second, third, andfourth valve transitions, thereby generating control information. Thecontrol information may be utilized in a subsequent compression cycle tocontrol timing of the first, second, third, and/or fourth valvetransitions of the subsequent compression cycle. The timing may becontrolled to maximize efficiency of the subsequent compression cycle.Gas may be thermally conditioned with heat-transfer fluid during atleast a portion of a compression cycle including or consistingessentially of the first, second, third, and fourth valve transitions.The thermal conditioning may render the gas compression substantiallyisothermal.

In yet another aspect, embodiments of the invention feature a method ofincreasing efficiency of an energy-storage process performed in acylinder assembly in which gas is compressed. The cylinder assembly isselectively fluidly connected to a high-side component by a high-sidevalve and selectively fluidly connected to a low-side component by alow-side valve. A plurality of compression cycles are performed withinthe cylinder assembly. Each compression cycle includes or consistsessentially of (i) performing a first valve transition by opening thelow-side valve to allow gas to enter the cylinder assembly from thelow-side component, (ii) performing a second valve transition by closingthe low-side valve, the gas within the cylinder assembly beingcompressed thereafter, (iii) performing a third valve transition byopening the high-side valve to allow a portion of the compressed gas toenter the high-side component from the cylinder assembly, a remnantportion of the gas remaining in the cylinder assembly thereafter, and(iv) performing a fourth valve transition by closing the high-sidevalve, the remnant portion of the gas within the cylinder assemblyexpanding thereafter. During each compression cycle, the timing of thefirst second, third, and/or fourth valve transitions are altered tomaximize efficiency of the compression cycle. The timing may be alteredbased at least in part on control information generated during aprevious compression cycle. The control information may include orconsist essentially of a temperature within the cylinder assembly, apressure within the cylinder assembly, a position of a boundarymechanism within the cylinder assembly, the pressure of the high-sidecomponent, and/or the pressure of the low-side component.

In an aspect, embodiments of the invention feature an energy storage andrecovery system including or consisting essentially of a cylinderassembly for expanding gas to recover energy and/or compressing gas tostore energy, a high-side component selectively fluidly connected to thecylinder assembly, a low-side component selectively fluidly connected tothe cylinder assembly, and a control system. The high-side componentsupplies gas to the cylinder assembly for expansion therein and/oraccepts gas from the cylinder assembly after compression therein. Thelow-side component supplies gas to the cylinder assembly for compressiontherein and/or accepts gas from the cylinder assembly after expansiontherein.

The control system may operate the cylinder assembly to (i) perform afirst valve transition by opening the low-side valve to allow gas toenter the cylinder assembly from the low-side component, the cylinderassembly containing gas at a first pressure prior to the first valvetransition, (ii) perform a second valve transition by closing thelow-side valve, the gas within the cylinder assembly being compressedthereafter, (iii) perform a third valve transition by opening thehigh-side valve to allow a portion of the compressed gas to enter thehigh-side component from the cylinder assembly, where (a) a remnantportion of the gas remains in the cylinder assembly after the thirdvalve transition and (b) the compressed gas is at a second pressureprior to the third valve transition, (iv) perform a fourth valvetransition by closing the high-side valve, the remnant portion of thegas within the cylinder assembly expanding thereafter to approximatelythe first pressure, and (v) enforce a transition restriction includingor consisting essentially of (a) performing the first valve transitiononly when the first pressure is approximately equal to a pressure of thelow-side component and/or (b) performing the third valve transition onlywhen the second pressure is approximately equal to a pressure of thehigh-side component.

The control system may operate the cylinder assembly to (i) perform afirst valve transition by opening the low-side valve to allow gas toenter the cylinder assembly from the low-side component, the cylinderassembly containing gas at a first pressure prior to the first valvetransition, (ii) perform a second valve transition by closing thelow-side valve, the gas within the cylinder assembly being compressedthereafter, (iii) perform a third valve transition by opening thehigh-side valve to allow a portion of the compressed gas to enter thehigh-side component from the cylinder assembly, where (a) a remnantportion of the gas remains in the cylinder assembly after the thirdvalve transition and (b) the compressed gas is at a second pressureprior to the third valve transition, (iv) perform a fourth valvetransition by closing the high-side valve, the remnant portion of thegas within the cylinder assembly expanding thereafter to approximatelythe first pressure, and (v) enforce a transition restriction includingor consisting essentially of (i) performing the first valve transitiononly when the first pressure is approximately equal to a pressure of thelow-side component and/or (ii) performing the third valve transitiononly when the second pressure is approximately equal to a pressure ofthe high-side component.

In another aspect, embodiments of the invention feature an energystorage and recovery system including or consisting essentially of acylinder assembly for expanding gas to recover energy and/or compressinggas to store energy, a high-side component selectively fluidly connectedto the cylinder assembly, a low-side component selectively fluidlyconnected to the cylinder assembly, and a control system. The high-sidecomponent supplies gas to the cylinder assembly for expansion thereinand/or accepts gas from the cylinder assembly after compression therein.The low-side component supplies gas to the cylinder assembly forcompression therein and/or accepts gas from the cylinder assembly afterexpansion therein.

The control system may operate the cylinder assembly to perform, withinthe cylinder assembly, a plurality of expansion cycles each including orconsisting essentially of (i) performing a first valve transition byopening the high-side valve to allow compressed gas to enter thecylinder assembly from the high-side component, (ii) performing a secondvalve transition by closing the high-side valve, the gas within thecylinder assembly expanding thereafter, (iii) performing a third valvetransition by opening the low-side valve to allow a portion of theexpanded gas to enter the low-side component from the cylinder assembly,a remnant portion of the gas remaining in the cylinder assembly afterthe third valve transition, and (iv) performing a fourth valvetransition by closing the low-side valve, the remnant portion of the gaswithin the cylinder assembly being compressed thereafter. The controlsystem may also, during each expansion cycle, alter a timing of thefirst, second, third, and/or fourth valve transitions to maximizeefficiency of the expansion cycle.

The control system may operate the cylinder assembly to perform, withinthe cylinder assembly, a plurality of compression cycles each includingor consisting essentially of (i) performing a first valve transition byopening the low-side valve to allow gas to enter the cylinder assemblyfrom the low-side component, (ii) performing a second valve transitionby closing the low-side valve, the gas within the cylinder assemblybeing compressed thereafter, (iii) performing a third valve transitionby opening the high-side valve to allow a portion of the compressed gasto enter the high-side component from the cylinder assembly, a remnantportion of the gas remaining in the cylinder assembly thereafter, and(iv) performing a fourth valve transition by closing the high-sidevalve, the remnant portion of the gas within the cylinder assemblyexpanding thereafter. The control system may also, during eachcompression cycle, alter a timing of the first, second, third, and/orfourth valve transitions to maximize efficiency of the compressioncycle.

These and other objects, along with advantages and features of theinvention, will become more apparent through reference to the followingdescription, the accompanying drawings, and the claims. Furthermore, itis to be understood that the features of the various embodimentsdescribed herein are not mutually exclusive and can exist in variouscombinations and permutations. Note that as used herein, the terms“pipe,” “piping” and the like shall refer to one or more conduits thatare rated to carry gas or liquid between two points. Thus, the singularterm should be taken to include a plurality of parallel conduits whereappropriate. Herein, the terms “liquid” and “water” interchangeablyconnote any mostly or substantially incompressible liquid, the terms“gas” and “air” are used interchangeably, and the term “fluid” may referto a liquid, a gas, or a mixture of liquid and gas (e.g., a foam) unlessotherwise indicated. As used herein unless otherwise indicated, theterms “approximately” and “substantially” mean±10%, and, in someembodiments, ±5%. A “valve” is any mechanism or component forcontrolling fluid communication between fluid paths or reservoirs, orfor selectively permitting control or venting. The term “cylinder”refers to a chamber, of uniform but not necessarily circularcross-section, which may contain a slidably disposed piston or othermechanism that separates the fluid on one side of the chamber from thaton the other, preventing fluid movement from one side of the chamber tothe other while allowing the transfer of force/pressure from one side ofthe chamber to the next or to a mechanism outside the chamber. At leastone of the two ends of a chamber may be closed by end caps, also hereintermed “heads.” As utilized herein, an “end cap” is not necessarily acomponent distinct or separable from the remaining portion of thecylinder, but may refer to an end portion of the cylinder itself. Rods,valves, and other devices may pass through the end caps. A “cylinderassembly” may be a simple cylinder or include multiple cylinders, andmay or may not have additional associated components (such as mechanicallinkages among the cylinders). The shaft of a cylinder may be coupledhydraulically or mechanically to a mechanical load (e.g., a hydraulicmotor/pump or a crankshaft) that is in turn coupled to an electricalload (e.g., rotary or linear electric motor/generator attached to powerelectronics and/or directly to the grid or other loads), as described inthe '678 and '842 patents. As used herein, “thermal conditioning” of aheat-exchange fluid does not include any modification of the temperatureof the heat-exchange fluid resulting from interaction with gas withwhich the heat-exchange fluid is exchanging thermal energy; rather, suchthermal conditioning generally refers to the modification of thetemperature of the heat-exchange fluid by other means (e.g., an externalheat exchanger). The terms “heat-exchange” and “heat-transfer” aregenerally utilized interchangeably herein. Unless otherwise indicated,motor/pumps described herein are not required to be configured tofunction both as a motor and a pump if they are utilized during systemoperation only as a motor or a pump but not both. Gas expansionsdescribed herein may be performed in the absence of combustion (asopposed to the operation of an internal-combustion cylinder, forexample).

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. Cylinders, rods, and othercomponents are depicted in cross section in a manner that will beintelligible to all persons familiar with the art of pneumatic andhydraulic cylinders. Also, the drawings are not necessarily to scale,emphasis instead generally being placed upon illustrating the principlesof the invention. In the following description, various embodiments ofthe present invention are described with reference to the followingdrawings, in which:

FIG. 1 is a schematic drawing of a compressed-gas energy storage systemin accordance with various embodiments of the invention;

FIG. 2 is a schematic drawing of various components of a compressed-gasenergy storage system in accordance with various embodiments of theinvention;

FIG. 3 is a schematic drawing of the major components of a compressedair energy storage and recovery system in accordance with variousembodiments of the invention;

FIG. 4 is a schematic drawing of various components of a multi-cylindercompressed-gas energy storage system in accordance with variousembodiments of the invention;

FIG. 5 is a schematic drawing of a cylinder assembly with apparatus forthe generation of foam external to the cylinder in accordance withvarious embodiments of the invention;

FIG. 6 is a schematic drawing of a cylinder assembly with apparatus forthe generation of foam external to the cylinder and provision forbypassing the foam-generating apparatus in accordance with variousembodiments of the invention;

FIG. 7 is a schematic drawing of a cylinder assembly with apparatus forthe generation of foam in a vessel external to the cylinder inaccordance with various embodiments of the invention;

FIG. 8 is a schematic drawing of a cylinder assembly with apparatus forthe generation of foam internal to the cylinder in accordance withvarious embodiments of the invention;

FIG. 9 is a schematic drawing of a compressed-air energy storage systememploying multiple pairs of high- and low-pressure cylinders inaccordance with various embodiments of the invention;

FIG. 10 is an illustrative plot of pressure as a function of time forfour different expansion scenarios in accordance with variousembodiments of the invention;

FIG. 11 is a graphical display of experimental test data in accordancewith various embodiments of the invention;

FIG. 12 is an illustrative plot of the ideal pressure-volume cycle in acylinder operated as either a compressor or expander;

FIG. 13 is an illustrative plot of cylinder chamber pressure as afunction of cylinder chamber volume for three different expansionscenarios in an illustrative CAES system in accordance with variousembodiments of the invention;

FIGS. 14A-14C are illustrative plots of cylinder chamber pressure as afunction of cylinder chamber volume for different expansion scenarios inan illustrative CAES system in accordance with various embodiments ofthe invention;

FIG. 15 is an illustrative plot of cylinder chamber pressure as afunction of cylinder chamber volume for three different compressionscenarios in an illustrative CAES system in accordance with variousembodiments of the invention; and

FIG. 16 is an illustrative plot of cylinder chamber pressure as afunction of cylinder chamber volume for three different compressionscenarios in an illustrative CAES system in accordance with variousembodiments of the invention.

DETAILED DESCRIPTION

FIG. 1 depicts an illustrative system 100 that may be part of a largersystem, not otherwise depicted, for the storage and release of energy.Subsequent figures will clarify the application of embodiments of theinvention to such a system. The system 100 depicted in FIG. 1 featuresan assembly 101 for compressing and expanding gas. Expansion/compressionassembly 101 may include or consist essentially of either one or moreindividual devices for expanding or compressing gas (e.g., turbines orcylinder assemblies that each may house a movable boundary mechanism) ora staged series of such devices, as well as ancillary devices (e.g.,valves) not depicted explicitly in FIG. 1.

An electric motor/generator 102 (e.g., a rotary or linear electricmachine) is in physical communication (e.g., via hydraulic pump, pistonshaft, or mechanical crankshaft) with the expansion/compression assembly101. The motor/generator 102 may be electrically connected to a sourceand/or sink of electric energy not explicitly depicted in FIG. 1 (e.g.,an electrical distribution grid or a source of renewable energy such asone or more wind turbines or solar cells).

The expansion/compression assembly 101 may be in fluid communicationwith a heat-transfer subsystem 104 that alters the temperature and/orpressure of a fluid (i.e., gas, liquid, or gas-liquid mixture such as afoam) extracted from expansion/compression assembly 101 and, afteralteration of the fluid's temperature and/or pressure, returns at leasta portion of it to expansion/compression assembly 101. Heat-transfersubsystem 104 may include pumps, valves, and other devices (not depictedexplicitly in FIG. 1) ancillary to its heat-transfer function and to thetransfer of fluid to and from expansion/compression assembly 101.Operated appropriately, the heat-transfer subsystem 104 enablessubstantially isothermal compression and/or expansion of gas insideexpansion/compression assembly 101.

Connected to the expansion/compression assembly 101 is a pipe 106 with acontrol valve 108 that controls a flow of fluid (e.g., gas) betweenassembly 101 and a storage reservoir 112 (e.g., one or more pressurevessels, pipes, and/or caverns). The storage reservoir 112 may be influid communication with a heat-transfer subsystem 114 that alters thetemperature and/or pressure of fluid removed from storage reservoir 112and, after alteration of the fluid's temperature and/or pressure,returns it to storage reservoir 112. A second pipe 116 with a controlvalve 118 may be in fluid communication with the expansion/compressionassembly 101 and with a vent 120 that communicates with a body of gas atrelatively low pressure (e.g., the ambient atmosphere).

A control system 122 receives information inputs from any ofexpansion/compression assembly 101, storage reservoir 112, and othercomponents of system 100 and sources external to system 100. Theseinformation inputs may include or consist essentially of pressure,temperature, and/or other telemetered measurements of properties ofcomponents of system 101. Such information inputs, here genericallydenoted by the letter “T,” are transmitted to control system 122 eitherwirelessly or through wires. Such transmission is denoted in FIG. 1 bydotted lines 124, 126.

The control system 122 may selectively control valves 108 and 118 toenable substantially isothermal compression and/or expansion of a gas inassembly 101. Control signals, here generically denoted by the letter“C,” are transmitted to valves 108 and 118 either wirelessly or throughwires. Such transmission is denoted in FIG. 1 by dashed lines 128, 130.The control system 122 may also control the operation of theheat-transfer assemblies 104, 114 and of other components not explicitlydepicted in FIG. 1. The transmission of control and telemetry signalsfor these purposes is not explicitly depicted in FIG. 1.

The control system 122 may be any acceptable control device with ahuman-machine interface. For example, the control system 122 may includea computer (for example a PC-type) that executes a stored controlapplication in the form of a computer-readable software medium. Moregenerally, control system 122 may be realized as software, hardware, orsome combination thereof. For example, control system 122 may beimplemented on one or more computers, such as a PC having a CPU boardcontaining one or more processors such as the Pentium, Core, Atom, orCeleron family of processors manufactured by Intel Corporation of SantaClara, Calif., the 680x0 and POWER PC family of processors manufacturedby Motorola Corporation of Schaumburg, Ill., and/or the ATHLON line ofprocessors manufactured by Advanced Micro Devices, Inc., of Sunnyvale,Calif. The processor may also include a main memory unit for storingprograms and/or data relating to the methods described above. The memorymay include random access memory (RAM), read only memory (ROM), and/orFLASH memory residing on commonly available hardware such as one or moreapplication specific integrated circuits (ASIC), field programmable gatearrays (FPGA), electrically erasable programmable read-only memories(EEPROM), programmable read-only memories (PROM), programmable logicdevices (PLD), or read-only memory devices (ROM). In some embodiments,the programs may be provided using external RAM and/or ROM such asoptical disks, magnetic disks, or other storage devices.

For embodiments in which the functions of controller 122 are provided bysoftware, the program may be written in any one of a number ofhigh-level languages such as FORTRAN, PASCAL, JAVA, C, C++, C#, LISP,PERL, BASIC or any suitable programming language. Additionally, thesoftware can be implemented in an assembly language and/or machinelanguage directed to the microprocessor resident on a target device.

As described above, the control system 122 may receive telemetry fromsensors monitoring various aspects of the operation of system 100, andmay provide signals to control valve actuators, valves, motors, andother electromechanical/electronic devices. Control system 122 maycommunicate with such sensors and/or other components of system 100 (andother embodiments described herein) via wired or wireless communication.An appropriate interface may be used to convert data from sensors into aform readable by the control system 122 (such as RS-232 or network-basedinterconnects). Likewise, the interface converts the computer's controlsignals into a form usable by valves and other actuators to perform anoperation. The provision of such interfaces, as well as suitable controlprogramming, is clear to those of ordinary skill in the art and may beprovided without undue experimentation.

System 100 may be operated so as to compress gas admitted through thevent 120 and store the gas thus compressed in reservoir 112. Forexample, in an initial state of operation, valve 108 is closed and valve118 is open, admitting a quantity of gas into expansion/compressionassembly 101. When a desired quantity of gas has been admitted intoassembly 101, valve 118 may be closed. The motor/generator 102,employing energy supplied by a source not explicitly depicted in FIG. 1(e.g., the electrical grid), then provides mechanical power toexpansion/compression assembly 101, enabling the gas within assembly 101to be compressed.

During compression of the gas within assembly 101, fluid (i.e., gas,liquid, or a gas-liquid mixture) may be circulated between assembly 101and heat-exchange assembly 104. Heat-exchange assembly 104 may beoperated in such a manner as to enable substantially isothermalcompression of the gas within assembly 101. During or after compressionof the gas within assembly 101, valve 108 may be opened to enablehigh-pressure fluid (e.g., compressed gas or a mixture of liquid andcompressed gas) to flow to reservoir 112. Heat-exchange assembly 114 maybe operated at any time in such a manner as alter the temperature and/orpressure of the fluid within reservoir 112.

That system 100 may also be operated so as to expand compressed gas fromreservoir 112 in expansion/compression assembly 101 in such a manner asto deliver energy to the motor/generator 102 will be apparent to allpersons familiar with the operation of pneumatic, hydraulic, andelectric machines.

FIG. 2 depicts an illustrative system 200 that features a cylinderassembly 201 (i.e., an embodiment of assembly 101 in FIG. 1) incommunication with a reservoir 222 (112 in FIG. 1) and a vent toatmosphere 223 (120 in FIG. 1). In the illustrative system 200 shown inFIG. 2, the cylinder assembly 201 contains a piston 202 slidablydisposed therein. In some embodiments the piston 202 is replaced by adifferent boundary mechanism dividing cylinder assembly 201 intomultiple chambers, or piston 202 is absent entirely, and cylinderassembly 201 is a “liquid piston.” The cylinder assembly 201 may bedivided into, e.g., two pneumatic chambers or one pneumatic chamber andone hydraulic chamber. The piston 202 is connected to a rod 204, whichmay contain a center-drilled fluid passageway with fluid outlet 212extending from the piston 202. The rod 204 is also attached to, e.g., amechanical load (e.g., a crankshaft or a hydraulic system) that is notdepicted. The cylinder assembly 201 is in liquid communication with aheat-transfer subsystem 224 that includes or consists essentially of acirculation pump 214 and a spray mechanism 210 to enable substantiallyisothermal compression/expansion of gas. Heat-transfer fluid circulatedby pump 214 may be passed through a heat exchanger 203 (e.g.,tube-in-shell- or parallel-plate-type heat exchanger). Spray mechanism210 may include or consist essentially of one or more spray heads (e.g.,disposed at one end of cylinder assembly 201) and/or spray rods (e.g.,extending along at least a portion of the central axis of cylinderassembly 201). In other embodiments, the spray mechanism 210 is omittedand a foam, rather than a spray of droplets, is created to facilitateheat exchange between liquid and gas during compression and expansion ofgas within the cylinder assembly 201, as described in U.S. patentapplication Ser. No. 13/473,128, filed May 16, 2012 (the '128application), the entire disclosure of which is incorporated byreference herein. Foam may be generated by foaming gas withheat-exchange liquid in a mechanism (not shown, described in more detailbelow) external to the cylinder assembly 201 and then injecting theresulting foam into the cylinder assembly 201. Alternatively oradditionally, foam may be generated inside the cylinder assembly 201 bythe injection of heat-exchange liquid into cylinder assembly 201 througha foam-generating mechanism (e.g., spray head, rotating blade, one ormore nozzles), partly or entirely filling the pneumatic chamber ofcylinder assembly 201. In some embodiments, droplets and foams may beintroduced into cylinder assembly 201 simultaneously and/orsequentially. Various embodiments may feature mechanisms (not shown inFIG. 2) for controlling the characteristics of foam (e.g., bubble size)and for breaking down, separating, and/or regenerating foam.

System 200 further includes a first control valve 220 (108 in FIG. 1) incommunication with a storage reservoir 222 and cylinder assembly 201,and a second control valve 221 (118 in FIG. 1) in communication with avent 223 and cylinder assembly 201. A control system 226 (122 in FIG. 1)may control operation of, e.g., valves 222 and 221 based on varioussystem inputs (e.g., pressure, temperature, piston position, and/orfluid state) from cylinder assembly 201 and/or storage reservoir 222.Heat-transfer fluid (liquid or circulated by pump 214 enters throughpipe 213. Pipe 213 may be (a) connected to a low-pressure fluid source(e.g., fluid reservoir (not shown) at the pressure to which vent 223 isconnected or thermal well 242); (b) connected to a high-pressure source(e.g., fluid reservoir (not shown) at the pressure of reservoir 222);(c) selectively connected (using valve arrangement not shown) to lowpressure during a compression process and to high pressure during anexpansion process; (d) connected to changing-pressure fluid 208 in thecylinder 201 via connection 212; or (e) some combination of theseoptions.

In an initial state, the cylinder assembly 201 may contain a gas 206(e.g., air introduced to the cylinder assembly 201 via valve 221 andvent 223) and a heat-transfer fluid 208 (which may include or consistessentially of, e.g., water or another suitable liquid). When the gas206 enters the cylinder assembly 201, piston 202 is operated to compressthe gas 206 to an elevated pressure (e.g., approximately 3,000 psi).Heat-transfer fluid (not necessarily the identical body of heat-transferfluid 208) flows from pipe 213 to the pump 214. The pump 214 may raisethe pressure of the heat-exchange fluid to a pressure (e.g., up toapproximately 3,015 psig) somewhat higher than the pressure within thecylinder assembly 201, as described in the '409 application.Alternatively or in conjunction, embodiments of the invention add heat(i.e., thermal energy) to, or remove heat from, the high-pressure gas inthe cylinder assembly 201 by passing only relatively low-pressure fluidsthrough a heat exchanger or fluid reservoir, as detailed in U.S. patentapplication Ser. No. 13/211,440, filed Aug. 17, 2011 (the '440application), the entire disclosure of which is incorporated byreference herein.

Heat-transfer fluid is then sent through a pipe 216, where it may bepassed through a heat exchanger 203 (where its temperature is altered)and then through a pipe 218 to the spray mechanism 210. Theheat-transfer fluid thus circulated may include or consist essentiallyof liquid or foam. Spray mechanism 210 may be disposed within thecylinder assembly 201, as shown; located in the storage reservoir 222 orvent 223; or located in piping or manifolding around the cylinderassembly, such as pipe 218 or the pipes connecting the cylinder assemblyto storage reservoir 222 or vent 223. The spray mechanism 210 may beoperated in the vent 223 or connecting pipes during compression, and aseparate spray mechanism may be operated in the storage reservoir 222 orconnecting pipes during expansion. Heat-transfer spray 211 from spraymechanism 210 (and/or any additional spray mechanisms), and/or foam frommechanisms internal or external to the cylinder assembly 101, enablesubstantially isothermal compression of gas 206 within cylinder assembly201.

In some embodiments, the heat exchanger 203 is configured to conditionheat-transfer fluid at low pressure (e.g., a pressure lower than themaximum pressure of a compression or expansion stroke in cylinderassembly 201), and heat-transfer fluid is thermally conditioned betweenstrokes or only during portions of strokes, as detailed in the '440application. Embodiments of the invention are configured for circulationof heat-transfer fluid without the use of hoses that flex duringoperation through the use of, e.g., tubes or straws configured fornon-flexure and/or pumps (e.g., submersible bore pumps, axial flowpumps, or other in-line style pumps) internal to the cylinder assembly(e.g., at least partially disposed within the piston rod thereof), asdescribed in U.S. patent application Ser. No. 13/234,239, filed Sep. 16,2011 (the '239 application), the entire disclosure of which isincorporated by reference herein.

At or near the end of the compression stroke, control system 226 opensvalve 220 to admit the compressed gas 206 to the storage reservoir 222.Operation of valves 220 and 221 may be controlled by various inputs tocontrol system 226, such as piston position in cylinder assembly 201,pressure in storage reservoir 222, pressure in cylinder assembly 201,and/or temperature in cylinder assembly 201.

As mentioned above, the control system 226 may enforce substantiallyisothermal operation, i.e., expansion and/or compression of gas incylinder assembly 201, via control over, e.g., the introduction of gasinto and the exhausting of gas out of cylinder assembly 201, the ratesof compression and/or expansion, and/or the operation of theheat-exchange subsystem in response to sensed conditions. For example,control system 226 may be responsive to one or more sensors disposed inor on cylinder assembly 201 for measuring the temperature of the gasand/or the heat-exchange fluid within cylinder assembly 201, respondingto deviations in temperature by issuing control signals that operate oneor more of the system components noted above to compensate, in realtime, for the sensed temperature deviations. For example, in response toa temperature increase within cylinder assembly 201, control system 226may issue commands to increase the flow rate of spray 211 ofheat-exchange fluid 208.

Furthermore, embodiments of the invention may be applied to systems inwhich cylinder assembly 201 (or a chamber thereof) is in fluidcommunication with a pneumatic chamber of a second cylinder (e.g., asshown in FIG. 4). That second cylinder, in turn, may communicatesimilarly with a third cylinder, and so forth. Any number of cylindersmay be linked in this way. These cylinders may be connected in parallelor in a series configuration, where the compression and expansion isdone in multiple stages.

The fluid circuit of heat exchanger 203 may be filled with water, acoolant mixture, an aqueous foam, or any other acceptable heat-exchangemedium. In alternative embodiments, a gas, such as air or refrigerant,is used as the heat-exchange medium. In general, the fluid is routed byconduits to a large reservoir of such fluid in a closed or open loop.One example of an open loop is a well or body of water from whichambient water is drawn and the exhaust water is delivered to a differentlocation, for example, downstream in a river. In a closed-loopembodiment, a cooling tower may cycle the water through the air forreturn to the heat exchanger. Likewise, water may pass through asubmerged or buried coil of continuous piping where a counterheat-exchange occurs to return the fluid flow to ambient temperaturebefore it returns to the heat exchanger for another cycle.

In various embodiments, the heat-exchange fluid is conditioned (i.e.,pre-heated and/or pre-chilled) or used for heating or cooling needs byconnecting the fluid inlet 238 and fluid outlet 240 of the externalheat-exchange side of the heat exchanger 203 to an installation such asa heat-engine power plant, an industrial process with waste heat, a heatpump, and/or a building needing space heating or cooling, as describedin the '731 patent. Alternatively, the external heat-exchange side ofthe heat exchanger 203 may be connected to a thermal well 242 asdepicted in FIG. 2. The thermal well 242 may include or consistessentially of a large water reservoir that acts as aconstant-temperature thermal fluid source for use with the system.Alternatively, the water reservoir may be thermally linked to waste heatfrom an industrial process or the like, as described above, via anotherheat exchanger contained within the installation. This allows theheat-exchange fluid to acquire or expel heat from/to the linked process,depending on configuration, for later use as a heating/cooling medium inthe energy storage/conversion system. Alternatively, the thermal well242 may include two or more bodies of energy-storage medium, e.g., ahot-water thermal well and a cold-water thermal well, that are typicallymaintained in contrasting energy states in order to increase the exergyof system 200 compared with a system in which thermal well 242 includesa single body of energy-storage medium. Storage media other than watermay be utilized in the thermal well 242; temperature changes, phasechanges, or both may be employed by storage media of thermal well 242 tostore and release energy. Thermal or fluid links (not shown) to theatmosphere, ground, and/or other components of the environment may alsobe included in system 200, allowing mass, thermal energy, or both to beadded to or removed from the thermal well 242. Moreover, as depicted inFIG. 2, the heat-transfer subsystem 224 does not interchange fluiddirectly with the thermal well 242, but in other embodiments, fluid ispassed directly between the heat-transfer subsystem 224 and the thermalwell 242 with no heat exchanger maintaining separation between fluids.

FIG. 3 is a schematic of the major components of an illustrative system300 that employs a pneumatic cylinder 302 to efficiently convert (i.e.,store) mechanical energy into the potential energy of compressed gasand, in another mode of operation, efficiently convert (i.e., recover)the potential energy of compressed gas into mechanical work. Thepneumatic cylinder 302 may contain a slidably disposed piston 304 thatdivides the interior of the cylinder 302 into a distal chamber 306 and aproximal chamber 308. A port or ports (not shown) with associated pipes312 and a bidirectional valve 316 enables gas from a high-pressurestorage reservoir 320 to be admitted to chamber 306 as desired. A portor ports (not shown) with associated pipes 322 and a bidirectional valve324 enables gas from the chamber 306 to be exhausted through a vent 326to the ambient atmosphere as desired. In alternate embodiments, vent 326is replaced by additional lower-pressure pneumatic cylinders (orpneumatic chambers of cylinders). A port or ports (not shown) enablesthe interior of the chamber 308 to communicate freely at all times withthe ambient atmosphere. In alternate embodiments, cylinder 302 isdouble-acting and chamber 308 is, like chamber 306, equipped to admitand exhaust fluids in various states of operation. The distal end of arod 330 is coupled to the piston 304. The rod 330 may be connected to acrankshaft, hydraulic cylinder, or other mechanisms for convertinglinear mechanical motion to useful work as described in the '678 and'842 patents.

In the energy recovery or expansion mode of operation, storage reservoir320 is filled with high-pressure air (or other gas) 332 and a quantityof heat-transfer fluid 334. The heat-transfer fluid 334 may be anaqueous foam or a liquid that tends to foam when sprayed or otherwiseacted upon. The liquid component of the aqueous foam, or the liquid thattends to foam, may include or consist essentially of water with 2% to 5%of certain additives; these additives may also provide functions ofanti-corrosion, anti-wear (lubricity), anti-biogrowth (biocide),freezing-point modification (anti-freeze), and/or surface-tensionmodification. Additives may include a micro-emulsion of a lubricatingfluid such as mineral oil, a solution of agents such as glycols (e.g.propylene glycol), or soluble synthetics (e.g. ethanolamines). Suchadditives tend to reduce liquid surface tension and lead to substantialfoaming when sprayed. Commercially available fluids may be used at anapproximately 5% solution in water, such as Mecagreen 127 (availablefrom the Condat Corporation of Michigan), which consists in part of amicro-emulsion of mineral oil, and Quintolubric 807-WP (available fromthe Quaker Chemical Corporation of Pennsylvania), which consists in partof a soluble ethanolamine. Other additives may be used at higherconcentrations (such as at a 50% solution in water), including Cryo-tek100/A1 (available from the Hercules Chemical Company of New Jersey),which consists in part of a propylene glycol. These fluids may befurther modified to enhance foaming while being sprayed and to speeddefoaming when in a reservoir.

The heat-transfer fluid 334 may be circulated within the storagereservoir 320 via high-inlet-pressure, low-power-consumption pump 336(such as described in the '731 patent). In various embodiments, thefluid 334 may be removed from the bottom of the storage reservoir 320via piping 338, circulated via pump 336 through a heat exchanger 340,and introduced (e.g., sprayed) back into the top of storage reservoir320 via piping 342 and spray head 344 (or other suitable mechanism). Anychanges in pressure within reservoir 320 due to removal or addition ofgas (e.g., via pipe 312) generally tend to result in changes intemperature of the gas 332 within reservoir 320. By spraying and/orfoaming the fluid 334 throughout the storage reservoir gas 332, heat maybe added to or removed from the gas 332 via heat exchange with theheat-transfer fluid 334. By circulating the heat-transfer fluid 334through heat exchanger 340, the temperature of the fluid 334 and gas 332may be kept substantially constant (i.e., isothermal). Counterflowheat-exchange fluid 346 at near-ambient pressure may be circulated froma near-ambient-temperature thermal well (not shown) or source (e.g.,waste heat source) or sink (e.g., cold water source) of thermal energy,as described in more detail below.

In various embodiments of the invention, reservoir 320 contains anaqueous foam, either unseparated or partially separated into its gaseousand liquid components. In such embodiments, pump 336 may circulateeither the foam itself, or the separated liquid component of the foam,or both, and recirculation of fluid into reservoir 320 may includeregeneration of foam by apparatus not shown in FIG. 3.

In the energy recovery or expansion mode of operation, a quantity of gasmay be introduced via valve 316 and pipe 312 into the upper chamber 306of cylinder 302 when piston 304 is near or at the top of its stroke(i.e., “top dead center” of cylinder 302). The piston 304 and its rod330 will then be moving downward (the cylinder 302 may be orientedarbitrarily but is shown vertically oriented in this illustrativeembodiment). Heat-exchange fluid 334 may be introduced into chamber 306concurrently via optional pump 350 (alternatively, a pressure drop maybe introduced in line 312 such that pump 350 is not needed) through pipe352 and directional valve 354. This heat-exchange fluid 334 may besprayed into chamber 306 via one or more spray nozzles 356 in such amanner as to generate foam 360. (In some embodiments, foam 360 isintroduced directly into chamber 306 in foam form.) The foam 360 mayentirely fill the entire chamber 306, but is shown in FIG. 3, forillustrative purposes only, as only partially filling chamber 306.Herein, the term “foam” denotes either (a) foam only or (b) any of avariety of mixtures of foam and heat-exchange liquid in other,non-foaming states (e.g., droplets). Moreover, some non-foamed liquid(not shown) may accumulate at the bottom of chamber 306; any such liquidis generally included in references herein to the foam 360 withinchamber 306.

System 300 is instrumented with pressure, piston position, and/ortemperature sensors (not shown) and controlled via control system 362.At a predetermined position of piston 304, an amount of gas 332 andheat-transfer fluid 334 have been admitted into chamber 306 and valve316 and valve 354 are closed. (Valves 316 and 354 may close at the sametime or at different times, as each has a control value based onquantity of fluid desired.) The gas in chamber 306 then undergoes freeexpansion, continuing to drive piston 304 downward. During thisexpansion, in the absence of foam 360, the gas would tend to decreasesubstantially in temperature. With foam 360 largely or entirely fillingthe chamber, the temperature of the gas in chamber 306 and thetemperature of the heat-transfer fluid 360 tend to approximate to eachother via heat exchange. The heat capacity of the liquid component ofthe foam 360 (e.g., water with one or more additives) may be much higherthan that of the gas (e.g., air) such that the temperature of the gasand liquid do not change substantially (i.e., are substantiallyisothermal) even over a many-times gas expansion (e.g., from 250 psig tonear atmospheric pressure, or in other embodiments from 3,000 psig to250 psig).

When the piston 304 reaches the end of its stroke (bottom dead center),the gas within chamber 306 will have expanded to a predetermined lowerpressure (e.g., near atmospheric). Valve 324 will then be opened,allowing gas from chamber 306 to be vented, whether to atmospherethrough pipe 322 and vent 326 (as illustrated here) or, in otherembodiments, to a next stage in the expansion process (e.g., chamber ina separate cylinder), via pipe 322. Valve 324 remains open as the pistonundergoes an upward (i.e., return) stroke, emptying chamber 306. Part orsubstantially all of foam 360 is also forced out of chamber 306 via pipe322. A separator (not shown) or other means such as gravity separationis used to recover heat-transfer fluid, preferably de-foamed (i.e., as asimple liquid with or without additives), and to direct it into astorage reservoir 364 via pipe 366.

When piston 304 reaches top of stroke again, the process repeats withgas 332 and heat-transfer fluid 334 admitted from vessel 320 via valves316 and 354. If additional heat-transfer fluid is needed in reservoir320, it may be pumped back into reservoir 320 from reservoir 364 viapiping 367 and optional pump/motor 368. In one mode of operation, pump368 may be used to continuously refill reservoir 320 such that thepressure in reservoir 320 is held substantially constant. That is, asgas is removed from reservoir 320, heat-transfer fluid 334 is added tomaintain constant pressure in reservoir 320. In other embodiments, pump368 is not used or is used intermittently, the pressure in reservoir 320continues to decrease during an energy-recovery process (i.e., involvingremoval of gas from reservoir 320), and the control system 362 changesthe timing of valves 316 and 354 accordingly so as to reachapproximately the same ending pressure when the piston 304 reaches theend of its stroke. An energy-recovery process may continue until thestorage reservoir 320 is nearly empty of pressurized gas 332, at whichtime an energy-storage process may be used to recharge the storagereservoir 320 with pressurized gas 332. In other embodiments, theenergy-recovery and energy-storage processes are alternated based onoperator requirements.

In either the energy-storage or energy-compression mode of operation,storage reservoir 320 is typically at least partially depleted ofhigh-pressure gas 332, as storage reservoir 320 also typically containsa quantity of heat-transfer fluid 334. Reservoir 364 is at low pressure(e.g., atmospheric or some other low pressure that serves as the intakepressure for the compression phase of cylinder 302) and contains aquantity of heat-transfer fluid 370.

The heat-transfer fluid 370 may be circulated within the reservoir 364via low-power-consumption pump 372. In various embodiments, the fluid370 may be removed from the bottom of the reservoir 364 via piping 367,circulated via pump 372 through a heat exchanger 374, and introduced(e.g., sprayed) back into the top of reservoir 364 via piping 376 andspray head 378 (or other suitable mechanism). By spraying the fluid 370throughout the reservoir gas 380, heat may be added or removed from thegas via the heat-transfer fluid 370. By circulating the heat-transferfluid 370 through heat exchanger 374, the temperature of the fluid 370and gas 380 may be kept near constant (i.e., isothermal). Counterflowheat-exchange fluid 382 at near-ambient pressure may be circulated froma near-ambient-temperature thermal well (not shown) or source (e.g.,waste heat source) or sink (e.g., cold water source) of thermal energy.In one embodiment, counterflow heat-exchange fluid 382 is at hightemperature to increase energy recovery during expansion and/orcounterflow heat-exchange fluid 382 is at low temperature to decreaseenergy usage during compression.

In the energy-storage or compression mode of operation, a quantity oflow-pressure gas is introduced via valve 324 and pipe 322 into the upperchamber 306 of cylinder 302 starting when piston 304 is near top deadcenter of cylinder 302. The low-pressure gas may be from the ambientatmosphere (e.g., may be admitted through vent 326 as illustratedherein) or may be from a source of pressurized gas such as a previouscompression stage. During the intake stroke, the piston 304 and its rod330 will move downward, drawing in gas. Heat-exchange fluid 370 may beintroduced into chamber 306 concurrently via optional pump 384(alternatively, a pressure drop may be introduced in line 386 such thatpump 384 is not needed) through pipe 386 and directional valve 388. Thisheat exchange fluid 370 may be introduced (e.g., sprayed) into chamber306 via one or more spray nozzles 390 in such a manner as to generatefoam 360. This foam 360 may fill the chamber 306 partially or entirelyby the end of the intake stroke; for illustrative purposes only, foam360 is shown in FIG. 3 as only partially filling chamber 306. At the endof the intake stroke, piston 304 reaches the end-of-stroke position(bottom dead center) and chamber 306 is filled with foam 360 generatedfrom air at a low pressure (e.g., atmospheric) and heat-exchange liquid.

At the end of the stroke, with piston 304 at the end-of-stroke position,valve 324 is closed. Valve 388 is also closed, not necessarily at thesame time as valve 324, but after a predetermined amount ofheat-transfer fluid 370 has been admitted, creating foam 360. The amountof heat-transfer fluid 370 may be based upon the volume of air to becompressed, the ratio of compression, and/or the heat capacity of theheat-transfer fluid. Next, piston 304 and rod 330 are driven upwards viamechanical means (e.g., hydraulic fluid, hydraulic cylinder, mechanicalcrankshaft) to compress the gas within chamber 306.

During this compression, in the absence of foam 360, the gas in chamber306 would tend to increase substantially in temperature. With foam 360at least partially filling the chamber, the temperature of the gas inchamber 306 and the temperature of the liquid component of foam 360 willtend to equilibrate via heat exchange. The heat capacity of the fluidcomponent of foam 360 (e.g., water with one or more additives) may bemuch higher than that of the gas (e.g., air) such that the temperatureof the gas and fluid do not change substantially and are near-isothermaleven over a many-times gas compression (e.g., from near atmosphericpressure to 250 psig, or in other embodiments from 250 psig to 3,000psig).

The gas in chamber 306 (which includes, or consists essentially of, thegaseous component of foam 360) is compressed to a suitable pressure,e.g., a pressure approximately equal to the pressure within storagereservoir 320, at which time valve 316 is opened. The foam 360,including both its gaseous and liquid components, is then transferredinto storage reservoir 320 through valve 316 and pipe 312 by continuedupward movement of piston 304 and rod 330.

When piston 304 reaches top of stroke again, the process repeats, withlow-pressure gas and heat-transfer fluid 370 admitted from vent 326 andreservoir 364 via valves 324 and 388. If additional heat-transfer fluidis needed in reservoir 364, it may be returned to reservoir 364 fromreservoir 320 via piping 367 and optional pump/motor 368. Powerrecovered from motor 368 may be used to help drive the mechanicalmechanism for driving piston 304 and rod 330 or may be converted toelectrical power via an electric motor/generator (not shown). In onemode of operation, motor 368 may be run continuously, while reservoir320 is being filled with gas, in such a manner that the pressure inreservoir 320 is held substantially constant. That is, as gas is addedto reservoir 320, heat-transfer fluid 334 is removed from reservoir 320to maintain substantially constant pressure within reservoir 320. Inother embodiments, motor 368 is not used or is used intermittently; thepressure in reservoir 320 continues to increase during an energy-storageprocess and the control system 362 changes the timing of valves 316 and388 accordingly so that the desired ending pressure (e.g., atmospheric)is attained within chamber 306 when the piston 304 reaches bottom ofstroke. An energy-storage process may continue until the storagereservoir 320 is full of pressurized gas 332 at the maximum storagepressure (e.g., 3,000 psig), after which time the system is ready toperform an energy-recovery process. In various embodiments, the systemmay commence an energy-recovery process when the storage reservoir 320is only partly full of pressurized gas 332, whether at the maximumstorage pressure or at some storage pressure intermediate betweenatmospheric pressure and the maximum storage pressure. In otherembodiments, the energy-recovery and energy-storage processes arealternated based on operator requirements.

FIG. 4 depicts an illustrative system 400 that features at least twocylinder assemblies 402, 406 (i.e., an embodiment of assembly 101 inFIG. 1; e.g., cylinder assembly 201 in FIG. 2) and a heat-transfersubsystem 404, 408 (e.g., subsystem 224 in FIG. 2) associated with eachcylinder assembly 402, 406. Additionally, the system includes a thermalwell 410 (e.g., thermal well 242 in FIG. 2) which may be associated witheither or both of the heat-transfer subsystems 404, 408 as indicated bythe dashed lines.

Assembly 402 is in selective fluid communication with a storagereservoir 412 (e.g., 112 in FIG. 1, 222 in FIG. 2) capable of holdingfluid at relatively high pressure (e.g., approximately 3,000 psig).Assembly 406 is in selective fluid communication with assembly 402and/or with optional additional cylinder assemblies between assemblies402 and 406 as indicated by ellipsis marks 422. Assembly 406 is inselective fluid communication with an atmospheric vent 420 (e.g., 120 inFIG. 1, 223 in FIG. 2).

System 400 may compress air at atmospheric pressure (admitted to system400 through the vent 420) stagewise through assemblies 406 and 402 tohigh pressure for storage in reservoir 412. System 400 may also expandair from high pressure in reservoir 412 stagewise through assemblies 402and 406 to a low pressure (e.g., approximately 5 psig) for venting tothe atmosphere through vent 420.

As described in U.S. Pat. No. 8,191,362, filed Apr. 6, 2011 (the '362patent), the entire disclosure of which is incorporated by referenceherein, in a group of N cylinder assemblies used for expansion orcompression of gas between a high pressure (e.g., approximately 3,000psig) and a low pressure (e.g., approximately 5 psig), the system willcontain gas at N−1 pressures intermediate between the high-pressureextreme and the low pressure. Herein each such intermediate pressure istermed a “mid-pressure.” In illustrative system 400, N=2 and N−1=1, sothere is one mid-pressure (e.g., approximately 250 psig duringexpansion) in the system 400. In various states of operation of thesystem, mid-pressures may occur in any of the chambers of aseries-connected cylinder group (e.g., the cylinders of assemblies 402and 406) and within any valves, piping, and other devices in fluidcommunication with those chambers. In illustrative system 400, themid-pressure, herein denoted “mid-pressure P1,” occurs primarily invalves, piping, and other devices intermediate between assemblies 402and 406.

Assembly 402 is a high-pressure assembly: i.e., assembly 402 may admitgas at high pressure from reservoir 412 to expand the gas tomid-pressure P1 for transfer to assembly 402, and/or may admit gas atmid-pressure P1 from assembly 406 to compress the gas to high pressurefor transfer to reservoir 412. Assembly 406 is a low-pressure assembly:i.e., assembly 406 may admit gas at mid-pressure P1 from assembly 402 toexpand the gas to low pressure for transfer to the vent 420, and/or mayadmit gas at low pressure from vent 420 to compress the gas tomid-pressure P1 for transfer to assembly 402.

In system 400, extended cylinder assembly 402 communicates with extendedcylinder assembly 406 via a mid-pressure assembly 414. Herein, a“mid-pressure assembly” includes or consists essentially of a reservoirof gas that is placed in fluid communication with the valves, piping,chambers, and other components through or into which gas passes. The gasin the reservoir is at approximately at the mid-pressure which theparticular mid-pressure assembly is intended to provide. The reservoiris large enough so that a volume of mid-pressure gas approximately equalto that within the valves, piping, chambers, and other components withwhich the reservoir is in fluid communication may enter or leave thereservoir without substantially changing its pressure. Additionally, themid-pressure assembly may provide pulsation damping, additionalheat-transfer capability, fluid separation, and/or house one or moreheat-transfer sub-systems such as part or all of sub-systems 404 and/or408. As described in the '362 patent, a mid-pressure assembly maysubstantially reduce the amount of dead space in various components of asystem employing pneumatic cylinder assemblies, e.g., system 400 in FIG.4. Reduction of dead space tends to increase overall system efficiency.

Alternatively or in conjunction, pipes and valves (not shown in FIG. 4)bypassing mid-pressure assembly 414 may enable fluid to pass directlybetween assembly 402 and assembly 406. Valves 416, 418, 424, and 426control the passage of fluids between the assemblies 402, 406, 412, and414.

A control system 428 (e.g., 122 in FIG. 1, 226 in FIG. 2, 362 in FIG. 3)may control operation of, e.g., all valves of system 400 based onvarious system inputs (e.g., pressure, temperature, piston position,and/or fluid state) from assemblies 402 and 406, mid-pressure assembly414, storage reservoir 412, thermal well 410, heat transfer sub-systems404, 408, and/or the environment surrounding system 420.

It will be clear to persons reasonably familiar with the art ofpneumatic machines that a system similar to system 400 but differing bythe incorporation of one, two or more mid-pressure extended cylinderassemblies may be devised without additional undue experimentation. Itwill also be clear that all remarks herein pertaining to system 400 maybe applied to such an N-cylinder system without substantial revision, asindicated by elliptical marks 422. Such N-cylinder systems, though notdiscussed further herein, are contemplated and within the scope of theinvention. As shown and described in the '678 patent, N appropriatelysized cylinders, where N≧2, may reduce an original (single-cylinder)operating fluid pressure range R to R^(1/N) and correspondingly reducethe range of force acting on each cylinder in the N-cylinder system ascompared to the range of force acting in a single-cylinder system. Thisand other advantages, as set forth in the '678 patent, may be realizedin N-cylinder systems. Additionally, multiple identical cylinders may beadded in parallel and attached to a common or separate drive mechanism(not shown) with the cylinder assemblies 402, 406 as indicated byellipsis marks 432, 436, enabling higher power and air-flow rates.

FIG. 5 is a schematic diagram showing components of a system 500 forachieving approximately isothermal compression and expansion of a gasfor energy storage and recovery using a pneumatic cylinder 502 (shown inpartial cross-section) according to embodiments of the invention. Thecylinder 502 typically contains a slidably disposed piston 504 thatdivides the cylinder 502 into two chambers 506, 508. A reservoir 510contains gas at high pressure (e.g., 3,000 psi); the reservoir 510 mayalso contain a quantity of heat-exchange liquid 512. The heat-exchangeliquid 512 may contain an additive that increases the liquid's tendencyto foam (e.g., by lowering the surface tension of the liquid 512).Additives may include surfactants (e.g., sulfonates), a micro-emulsionof a lubricating fluid such as mineral oil, a solution of agents such asglycols (e.g., propylene glycol), or soluble synthetics (e.g.,ethanolamines). Foaming agents such as sulfonates (e.g., linear alkylbenzene sulfonate such as Bio-Soft D-40 available from Stepan Company ofIllinois) may be added, or commercially available foaming concentratessuch as firefighting foam concentrates (e.g., fluorosurfactant productssuch as those available from ChemGuard of Texas) may be used. Suchadditives tend to reduce liquid surface tension of water and lead tosubstantial foaming when sprayed. Commercially available fluids may beused at an approximately 5% solution in water, such as Mecagreen 127(available from the Condat Corporation of Michigan), which consists inpart of a micro-emulsion of mineral oil, and Quintolubric 807-WP(available from the Quaker Chemical Corporation of Pennsylvania), whichconsists in part of a soluble ethanolamine. Other additives may be usedat higher concentrations (such as at a 50% solution in water), includingCryo-tek 100/A1 (available from the Hercules Chemical Company of NewJersey), which consists in part of a propylene glycol. These fluids maybe further modified to enhance foaming while being sprayed and to speeddefoaming when in a reservoir.

A pump 514 and piping 516 may convey the heat-exchange liquid to adevice herein termed a “mixing chamber” (518). Gas from the reservoir510 may also be conveyed (via piping 520) to the mixing chamber 518.Within the mixing chamber 518, a foam-generating mechanism 522 combinesthe gas from the reservoir 510 and the liquid conveyed by piping 516 tocreate foam 524 of a certain grade (i.e., bubble size variance, averagebubble size, void fraction), herein termed Foam A, inside the mixingchamber 518.

The mixing chamber 518 may contain a screen 526 or other mechanism(e.g., source of ultrasound) to vary or homogenize foam structure.Screen 526 may be located, e.g., at or near the exit of mixing chamber518. Foam that has passed through the screen 526 may have a differentbubble size and other characteristics from Foam A and is herein termedFoam B (528). In other embodiments, the screen 526 is omitted, so thatFoam A is transferred without deliberate alteration to chamber 506.

The exit of the mixing chamber 518 is connected by piping 530 to a portin the cylinder 502 that is gated by a valve 532 (e.g., a poppet-stylevalve) that permits fluid from piping 530 to enter the upper chamber(air chamber) 506 of the cylinder 502. Valves (not shown) may controlthe flow of gas from the reservoir 510 through piping 520 to the mixingchamber 518, and from the mixing chamber 518 through piping 528 to theupper chamber 506 of the cylinder 502. Another valve 534 (e.g., apoppet-style valve) permits the upper chamber 506 to communicate withother components of the system 500, e.g., an additional separator device(not shown), the upper chamber of another cylinder (not shown), or avent to the ambient atmosphere (not shown).

The volume of reservoir 510 may be large (e.g., at least approximatelyfour times larger) relative to the volume of the mixing chamber 518 andcylinder 502. Foam A and Foam B are preferably statically stable foamsover a portion or all of the time-scale of typical cyclic operation ofsystem 500: e.g., for a 120 RPM system (i.e., 0.5 seconds perrevolution), the foam may remain substantially unchanged (e.g., lessthan 10% drainage) after 5.5 seconds or a time approximately five timesgreater than the revolution time.

In an initial state of operation of a procedure whereby gas stored inthe reservoir 510 is expanded to release energy, the valve 532 is open,the valve 534 is closed, and the piston 504 is near top dead center ofcylinder 502 (i.e., toward the top of the cylinder 502). Gas from thereservoir 510 is allowed to flow through piping 520 to the mixingchamber 518 while liquid from the reservoir 510 is pumped by pump 514 tothe mixing chamber 518. The gas and liquid thus conveyed to the mixingchamber 518 are combined by the foam-generating mechanism 522 to formFoam A (524), which partly or substantially fills the main chamber ofthe mixing chamber 518. Exiting the mixing chamber 518, Foam A passesthrough the screen 526, being altered thereby to Foam B. Foam B, whichis at approximately the same pressure as the gas stored in reservoir510, passes through valve 532 into chamber 506. In chamber 506, Foam Bexerts a force on the piston 504 that may be communicated to a mechanism(e.g., an electric generator, not shown) external to the cylinder 502 bya rod 536 that is connected to piston 504 and that passes slideablythrough the lower end cap of the cylinder 502.

The gas component of the foam in chamber 506 expands as the piston 504and rod 536 move downward. At some point in the downward motion ofpiston 504, the flow of gas from reservoir 510 into the mixing chamber518 and thence (as the gas component of Foam B) into chamber 506 may beended by appropriate operation of valves (not shown). As the gascomponent of the foam in chamber 506 expands, it will tend, unless heatis transferred to it, to decrease in temperature according to the IdealGas Law; however, if the liquid component of the foam in chamber 506 isat a higher temperature than the gas component of the foam in chamber506, heat will tend to be transferred from the liquid component to thegas component. Therefore, the temperature of the gas component of thefoam within chamber 506 will tend to remain constant (approximatelyisothermal) as the gas component expands.

When the piston 504 approaches bottom dead center of cylinder 502 (i.e.,has moved down to approximately its limit of motion), valve 532 may beclosed and valve 534 may be opened, allowing the expanded gas in chamber506 to pass from cylinder 502 to some other component of the system 500,e.g., a vent or a chamber of another cylinder for further expansion.

In some embodiments, pump 514 is a variable-speed pump, i.e., may beoperated so as to transfer liquid 512 at a slower or faster rate fromthe reservoir 510 to the foam-generating mechanism 522 and may beresponsive to signals from the control system (not shown). If the rateat which liquid 512 is transferred by the pump 514 to the foam-mechanism522 is increased relative to the rate at which gas is conveyed fromreservoir 510 through piping 520 to the mechanism 522, the void fractionof the foam produced by the mechanism 522 may be decreased. If the foamgenerated by the mechanism 522 (Foam A) has a relatively low voidfraction, the foam conveyed to chamber 506 (Foam B) will generally alsotend to have a relatively low void fraction. When the void fraction of afoam is lower, more of the foam consists of liquid, so more thermalenergy may be exchanged between the gas component of the foam and theliquid component of the foam before the gas and liquid components comeinto thermal equilibrium with each other (i.e., cease to change inrelative temperature). When gas at relatively high density (e.g.,ambient temperature, high pressure) is being transferred from thereservoir 510 to chamber 506, it may be advantageous to generate foamhaving a lower void fraction, enabling the liquid fraction of the foamto exchange a correspondingly larger quantity of thermal energy with thegas fraction of the foam.

All pumps shown in subsequent figures herein may also be variable-speedpumps and may be controlled based on signals from the control system.Signals from the control system may be based on system-performance(e.g., gas temperature and/or pressure, cycle time, etc.) measurementsfrom one or more previous cycles of compression and/or expansion.

Embodiments of the invention increase the efficiency of a system 500 forthe storage and retrieval of energy using compressed gas by enabling thesurface area of a given quantity of heat-exchange liquid 512 to begreatly increased (with correspondingly accelerated heat transferbetween liquid 512 and gas undergoing expansion or compression withincylinder 502) with less investment of energy than would be required byalternative methods of increasing the surface of area of the liquid,e.g., the conversion of the liquid 512 to a spray.

In other embodiments, the reservoir 510 is a separator rather than ahigh-pressure storage reservoir as depicted in FIG. 5. In suchembodiments, piping, valves, and other components not shown in FIG. 5are supplied that allow the separator to be placed in fluidcommunication with a high-pressure gas storage reservoir as well as withthe mixing chamber 518, as shown and described in the '128 application.

FIG. 6 is a schematic diagram showing components of a system 600 forachieving approximately isothermal compression and expansion of a gasfor energy storage and recovery using a pneumatic cylinder 604 (shown inpartial cross-section) according to embodiments of the invention. System600 is similar to system 500 in FIG. 5, except that system 600 includesa bypass pipe 638. Moreover, two valves 640, 642 are explicitly depictedin FIG. 6. Bypass pipe 638 may be employed as follows: (1) when gas isbeing released from the storage reservoir 610, mixed with heat-exchangeliquid 612 in the mixing chamber 618, and conveyed to chamber 606 ofcylinder 604 to be expanded therein, valve 640 will be closed and valve642 open; (2) when gas has been compressed in chamber 606 of cylinder604 and is to be conveyed to the reservoir 610 for storage, valve 640will be open and valve 642 closed. Less friction will tend to beencountered by fluids passing through valve 640 and bypass pipe 638 thanby fluids passing through valve 642 and screen 626 and around thefoam-generating mechanism 622. In other embodiments, valve 642 isomitted, allowing fluid to be routed through the bypass pipe 638 by thehigher resistance presented by the mixing chamber 618, and valve 640 isa check valve preventing fluid flow when gas is being released inexpansion mode. The direction of fluid flow from chamber 606 to thereservoir 610 via a lower-resistance pathway (i.e., the bypass pipe 638)will tend to result in lower frictional losses during such flow andtherefore higher efficiency for system 600.

In other embodiments, the reservoir 610 is a separator rather than ahigh-pressure storage reservoir as depicted in FIG. 6. In suchembodiments, piping, valves, and other components not shown in FIG. 6are supplied that allow the separator to be placed in fluidcommunication with a high-pressure gas storage reservoir as well as withthe mixing chamber 618 and bypass pipe 638.

FIG. 7 is a schematic diagram showing components of a system 700 forachieving approximately isothermal compression and expansion of a gasfor energy storage and recovery using a pneumatic cylinder 702 (shown inpartial cross-section) according to embodiments of the invention. System700 is similar to system 500 in FIG. 5, except that system 700 omits themixing chamber 518 and instead generates foam inside the storagereservoir 710. In system 700, a pump 714 circulates heat-exchange liquid712 to a foam-generating mechanism 722 (e.g., one or more spray nozzles)inside the reservoir 710. The reservoir 710 may, by means of the pump714 and mechanism 722, be filled partly or entirely by foam of aninitial or original character, Foam A (724). The reservoir 710 may beplaced in fluid communication via pipe 720 with a valve-gated port 744in cylinder 702. Valves (not shown) may govern the flow of fluid throughpipe 720. An optional screen 726 (or other suitable mechanism such as anultrasound source), shown in FIG. 7 inside pipe 720 but locatableanywhere in the path of fluid flow between reservoir 710 and chamber 706of the cylinder 702, serves to alter Foam A (724) to Foam B (728),regulating characteristics such as bubble-size variance and averagebubble size.

In other embodiments, the reservoir 710 is a separator rather than ahigh-pressure storage reservoir as depicted in FIG. 7. In suchembodiments, piping, valves, and other components not shown in FIG. 7will be supplied that allow the separator to be placed in fluidcommunication with a high-pressure gas storage reservoir as well as withthe cylinder 702. In other embodiments, a bypass pipe similar to thatdepicted in FIG. 6 is added to system 700 in order to allow fluid topass from cylinder 702 to reservoir 710 without passing through thescreen 726.

FIG. 8 is a schematic diagram showing components of a system 800 forachieving approximately isothermal compression and expansion of a gasfor energy storage and recovery using a pneumatic cylinder 802 (shown inpartial cross-section) according to embodiments of the invention. System800 is similar to system 500 in FIG. 5, except that system 800 omits themixing chamber 518 and instead generates foam inside the air chamber 806of the cylinder 802. In system 800, a pump 814 circulates heat-exchangeliquid 812 to a foam-generating mechanism 822 (e.g., one or more spraynozzles injecting into cylinder and/or onto a screen through whichadmitted air passes) either located within, or communicating with (e.g.,through a port), chamber 806. The chamber 806 may, by means of the pump814 and mechanism 822 (and by means of gas supplied from reservoir 810via pipe 820 through a port 844), be filled partly or substantiallyentirely by foam. The reservoir 810 may be placed in fluid communicationvia pipe 820 with valve-gated port 844 in cylinder 802. Valves (notshown) may govern the flow of fluid through pipe 820.

FIG. 9 is a schematic drawing of an illustrative CAES system 900employing pairs of high- and low-pressure cylinders in which air iscompressed and expanded. Half of the cylinders are high-pressurecylinders (HPCs, indicated in FIG. 900 by block 902) and half of thecylinders are low-pressure cylinders (LPCs, indicated in FIG. 900 byblock 904), resulting in a two-stage compression process. Block 902represents some number N of high-pressure cylinders (not shown) andblock 904 represents an equal number N of low-pressure cylinders (notshown). The HPCs and LPCs jointly drive a crankshaft that in turn drivesan electric generator or, in some states of operation of system 900, isdriven by an electric motor. Systems employing principles of operationsimilar to those of 900 but including other subsystems, othermechanisms, other arrangements of parts, other numbers of stages (i.e.,a single stage or more than one stage), and unequal numbers of high- andlow-pressure cylinders, are also contemplated and within the scope ofthe invention.

Separating the LPCs from the HPCs is a mid-pressure vessel (MPV) 906that buffers and decouples the HPCs 902 and LPCs 904 during eithercompression or expansion processes. This allows each cylinder assembly(i.e., each high- or low-pressure cylinder and the valves that controlthe entry or exit of gas from the cylinder) to operate independentlyfrom all the other cylinder assemblies within system 900. Independentoperation of cylinder assemblies allows, in turn, for optimization ofthe performance (e.g., optimization of valve timing) of each cylinderassembly. A system controller (not shown), e.g., a computerizedcontroller, coordinates the operation of individual cylinders with eachother and with the other pneumatic components and processes withinsystem 900.

In addition to the cylinders 902, 904 and MPV 906, system 900 alsoincludes a spray reservoir 908 that holds a heat-transfer fluid (e.g.,treated water) at low (e.g., atmospheric) pressure, a low-pressure spraychamber 910 that creates foam and/or spray at atmospheric pressure forintake into the LPCs for compression, and a high-pressure spray chamber912 that creates foam and/or spray at storage pressure (i.e., thepressure at which gas and/or heat-transfer fluid is stored aftercompression and/or before expansion) for expansions in the HPCs.Finally, system 900 includes one or more storage reservoirs (not shown)that are connected to the HPCs 902 via the high-pressure spray chamber912. The storage reservoirs typically contain compressed air, e.g., aircompressed by system 900 and stored for future expansion to driveelectricity generation.

Each of the cylinder assemblies in the HPC group 902 and LPC group 904typically includes a cylinder similar to cylinder 201 in FIG. 2, ahigh-side valve similar to valve 220 in FIG. 2, and a low-side valveassembly similar to valve 221 in FIG. 2. Each high-side valve includesor consists essentially of one or more poppet elements that open out ofthe cylinder, connecting the expansion/compression chamber of thecylinder to a volume that is generally at higher pressure than thechamber. For a low-pressure cylinder, the high-side valve connects thecylinder's expansion/compression chamber to the MPV 906; for ahigh-pressure cylinder, the high-side valve connects the cylinder'sexpansion/compression chamber to the high-pressure spray chamber 912.Because these high-side valves open out of the cylinder rather than intothe cylinder, they passively check open under an over-pressure conditionin the cylinder, reducing the risk of a hydrolocking event with possibleattendant damage to system components or interference with systemoperation.

Each low-side valve includes or consists essentially of one or morepoppet elements that open into the cylinder, connecting theexpansion/compression chamber of the cylinder to a volume that isgenerally at lower pressure than the chamber. For a low-pressurecylinder, the low-side valve connects the cylinder'sexpansion/compression chamber to the spray reservoir 908; for ahigh-pressure cylinder, the low-side valve connects the cylinder'sexpansion/compression chamber to the MPV 906. All of the valves, bothlow-side and high-side, may be hydraulically actuated. Other actuatedvalves such as variable cam-driven valves, electromagnetically actuatedvalves, mechanically actuated valves, and pneumatically actuated valvesare also considered and may be utilized.

The system 900 may cyclically perform a normal compression process (or“compression cycle”) or a normal expansion process (or “expansioncycle”). In a normal compression process, each low-pressure andhigh-pressure cylinder progresses through a series of four conditions orphases, each of which has an associated a valve configuration. The fourphases are (1) compression stroke, (2) direct fill, (3) regeneration orexpansion stroke, and (4) breathe, intake, or auxiliary stroke. Thenumbering of the phases is arbitrary in the sense that when the phasesare performed in a repeating cycle, no one phase is “first” other thanby convention. It is assumed in this description that all high-side andlow-side valves in system 900 activate instantaneously and ideally; theimplications of non-ideal valve actuation will be describedsubsequently. The four phases are described in detail below.

The compression stroke begins with the cylinder's piston at the bottomof its stroke range. The cylinder's expansion/compression chamber(herein also referred to simply as “the chamber”) is filled with air atrelatively low pressure (e.g., atmospheric). For example, the cylindermay have previously drawn in air through its low-side valve from asource on its low side (e.g., an HPC draws air in from the MPV 906, oran LPC draws air in from the ambient intake/exhaust port). With thepiston at bottom of stroke, the cylinder's low-side valve and high-sidevalve both close, if they were not already closed, and the piston beginsto move upward, compressing the air within the chamber: i.e., thecompression stroke begins. The compression stroke continues as thepiston moves up from bottom of stroke with both valves closed,compressing the air inside. The compression phase nominally ends whenthe pressure in the cylinder is approximately equal to the pressure inthe component (e.g., MPV 906 or HP spray chamber and thence tohigh-pressure storage reservoir) to which the cylinder is connected onits high side. At this point, the direct-fill stroke or phase begins.

The direct-fill stroke or phase occurs while the piston is still movingupward and involves pushing the compressed air within the chamber out ofthe cylinder and into the high-side component. Direct fill begins whenthe pressures in the cylinder and the high-side vessel are approximatelyequal and the high-side valve is actuated to open. The low-side valveremains closed. Once the high-side valve is open, the cylinder pushescompressed air from its chamber into the high-side component as thepiston continues to travel toward top of stroke. Direct fill ends whenthe cylinder reaches top of stroke, whereupon the high-side valve isclosed.

The regeneration stroke occurs with both valves closed as the cylinderpiston moves downward, away from top of stroke. Each cylinder has someamount of clearance volume, which is the physical space within thecylinder—above the piston and below the valves and in all theconnections and crevices—that is present when the piston is at top ofstroke. Moreover, in a CAES system that utilizes a liquid/water mixtureto effect heat transfer within the cylinder (e.g., system 900), somefraction of the clearance volume will be occupied by liquid and some byair. That portion of the clearance volume occupied by air during aparticular state of operation of the cylinder is the air dead volume(also herein termed simply the “dead volume”) of the cylinder in thatstate of operation. This is the portion of air that was compressedduring the compression stroke that was not then subsequently pushed intothe high-side component. This compressed air contains energy (i.e., boththermal and elastic potential), and the regeneration stroke allows thisenergy to be recaptured. The regeneration stroke starts at top of strokewith both valves closed and continues as the piston moves downward,expanding the dead volume air. The regeneration stroke ends when thepressure in the cylinder has dropped to the low-side vessel pressure andthe low-side valve is commanded open.

As the cylinder piston is moving downward, once the low-side valve isopened the intake stroke begins. The intake stroke continues, drawing innew air to be compressed on the next stroke, until the piston reachesbottom of stroke. At this point, the low-side valve is closed and thenext compression stroke may begin.

Each of the four compression stages is separated from preceding andsubsequent stages by a valve transition event, i.e., the opening orclosing of one or more valves. In the descriptions of the stages above,the valve transition points were clearly defined as top of stroke,bottom of stroke, or pressure equalization, but this assumes that thevalves of system 900 respond ideally and instantaneously. However,because of finite valve response time, each valve transition event is anopportunity for system optimization.

The first valve transition event mentioned above is the transition fromintake stroke to compression stroke, which nominally occurs at bottomdead center (BDC; the condition where the piston is at its nethermostpoint of motion). With finite (nonzero) valve response time, thelow-side valve will need to be commanded closed slightly before BDC andwill likely be full seat closed slightly after BDC. Transitioning thisvalve too early means that less air is drawn in than could have been,resulting in less air to be compressed during the following compressionstroke (reduced capacity). Transitioning the valve too late means thatsome of the air drawn in will be re-exhausted before the valve fullyseats, also resulting in reduced capacity.

The second valve event is at the end of compression, transitioning intodirect-fill, where the high-side valve is opened to end admission of airinto the chamber and start pushing air into the high-side vessel.Nominally, the high-side valve opens when the pressure in the chamber isequal to the pressure in the high-side component. However, because offinite valve response time, if the valve is commanded open when thepressures are equal, then the pressure in the chamber will spikesignificantly as the flow from the chamber is limited and throttledthrough the high-side valve while the valve is transitioning open. Thepressure spike may be avoided by commanding the high-side valve to openbefore pressures are equal in the chamber and the high-side component.However, if the high-side valve starts to open when the chamber pressureis still lower than that within the high-side component, then someamount of back-flow into the chamber will occur as fluid from thehigh-side component flows backward through the high-side valve into thechamber. (This backflow will be throttled, since the high-side valve ispartially open.) If the high-side valve is opened too early, then thepressure within the chamber will jump quickly to the high-side componentpressure, and the piston will need to perform additional work to pushthe air back out of the chamber into the high-side component. Thus, thisvalve transition entails a tradeoff between backflow and pressure-spike,both of which impact the pressure profile and the work that needs to beperformed by the piston upon the air.

The valve transition closing the high-side valve at the end of thedirect fill impacts system capacity. If the high-side valve is closedtoo early, then less air is pushed into the high-side component thancould have been, and the pressure will momentarily spike beforedropping. If the high-side valve is closed too late, then some of theair pushed into the high-side component will be pulled back out again asthe piston moves away from top dead center (TDC; the condition where thepiston is at its uppermost point of motion), and as the high-side valvefinishes closing the flow will be throttled so the energy of the airflowing back into the cylinder performs less work on the piston.Potential work lost to throttling is not, in general, recovered.

Finally, the transition at the end of the regeneration stroke that opensthe low-side valve to start the intake stroke impacts the work done onthe piston. If the low-side valve is opened too early, then theremaining air at higher pressure from the dead volume will no longerexpand, doing work on the piston, but will expand (throttled) throughthe opening low-side valve. If the low-side valve opens too late, thenthe pressure in the chamber will drop below the low-side componentpressure and the piston will have to do additional work to pull thepiston down and pull air through the partially open low-side valve.

Similarly, in a normal expansion process, each low-pressure andhigh-pressure cylinder progresses through a series of four conditions orsub-processes, each of which has an associated a valve configuration.The four conditions are (1) vent (or exhaust, or auxiliary) stroke, (2)pre-compression stroke, (3) direct drive, and (4) expansion stroke. Thenumbering of the phases is arbitrary in the sense that when the phasesare performed in a repeating cycle, no one phase is “first” other thanby convention. It is assumed in this description that all high-side andlow-side valves in system 900 activate instantaneously and ideally; theimplications of non-ideal valve actuation will be describedsubsequently. The four phases are described in detail below.

An expansion cycle begins at the bottom of stroke with the pistonbeginning to move upward from BDC and the low-side valve open,commencing a vent stroke. As the piston moves upward away from BDC, airin the chamber (e.g., air that was expanded in a previous cycle) isexhausted through the low-side valve to the low-side component (e.g.,exhausted from an HPC to the MPV 906 or from an LPC to the ambientintake/exhaust port). A vent stroke ends when the low-side valve isclosed and a pre-compression stroke begins. In general, the pistoncontinues to move upward without interruption as a vent stroke ends anda pre-compression stroke begins.

As the cylinder piston continues to move upward, before it reaches TDCthe low-side valve is closed to begin the pre-compression stroke. Inpre-compression, both the high-side valve and low-side valve are closedand the air volume trapped within the chamber is compressed. Incontrolling the events of pre-compression, a goal is to close off thelow-side valve at such a time that the air trapped in the chamber iscompressed as nearly as possible to the pressure of the cylinder'sadjoining high-side component when the piston reaches TDC. This allowsthe high-side valve to open at top of stroke with equal pressures oneither side, resulting in approximately zero throttled flow through thatvalve and approximately zero loss of exergy due to non-work-performingloss of pressure of a quantity of gas. Timing of the start ofpre-compression (closure of the low-side valve) greatly impacts theachievement of the equal-pressure goal.

Once the piston is at TDC and the high-side valve is opened, thedirect-drive stroke begins. In direct drive, the piston is moving down,away from TDC, and air in the high-side component is expanding andflowing through the high-side valve into the chamber, directly drivingthe piston downward. The direct drive stroke continues until anappropriate mass of air has been added to the cylinder, at which pointthe high-side valve closes and the expansion stroke begins. In general,the piston continues to move downward without interruption as adirect-drive stroke ends and an expansion stroke begins.

In an expansion stroke, both valves are closed, and the air that wasadmitted to the chamber during the direct-drive phase expands,continuing to perform work upon the piston as it drives it downward. Ifa correct mass of air was added to the cylinder during direct drive,then the air pressure at the end of the expansion stroke will beapproximately equal to the end-of-stroke target pressure at the momentwhen the piston reaches BDC. For a high-pressure cylinder, theend-of-stroke target pressure is the pressure in the MPV; for alow-pressure cylinder, the end-of-stroke target pressure is the ventpressure, which is typically slightly higher than atmospheric pressure.Once the piston reaches BDC, the low-side valve is opened and thecylinder begins to move up in the next vent stroke.

Valve actuation timings during a compression or expansion cycle may havea significant impact on the efficiency of the cycle. Such impact tends,in some embodiments, to be greater during an expansion cycle than duringa compression cycle. During an expansion cycle, the first valvetransition, as described hereinabove, is the closing of the low-sidevalve to begin the pre-compression. Incorrect or suboptimal timing ofthis valve transition may have significant consequences for the cycle.First, this valve transition is associated with the need for rapidhigh-side valve transition (short actuation time): as the valve isclosing, the pressure in the chamber is rising quickly, resulting inthrottled flow through the valve during the transition. Thus, the slowerthe transition, the greater the flow losses. Second, if the valve isclosed later than is ideal, there will be less air in the cylinder tocompress and less stroke length during which to compress it, resultingin a pressure at TDC less than the pressure in the high-side vessel. Ifthis difference is large enough, then the pressure will be below theminimum coupling pressure and the high-side valve will be physicallyunable to open (i.e., the actuator will not be able to provide enoughforce to open the valve against the pressure difference) and thecylinder will not be able to complete the expansion cycle. If thepressure at TDC is above the minimum coupling pressure but below thepressure within the high-side component, then the high-side valve willbe able to open, but gas will flow into the cylinder during the openingevent without performing useful work on the piston. Contrariwise, if thelow-side valve closing at the start of the pre-compression occurs tooearly, then the pressure within the chamber will reach the pressurewithin the high-side component before the piston reaches TDC, andsurpass the pressure within the high-side component by the time thepiston reaches TDC. In this case, more air would have been re-compressedthan necessary (and less air would have been exhausted), resulting in acapacity reduction. If the pressure in the chamber reaches the high-sidevessel before TDC, then the high-side valve should open when thepressures are equal rather than waiting to TDC, in order to preventover-pressurization of the cylinder.

Once the high-side valve is open at TDC and the cylinder is in directdrive, with the piston moving down, the next transition is the closingof the high-side valve at the end of direct drive. This transition mayimpact both capacity and efficiency. Under perfect valve timing (i.e.,closure of the high-side valve occurs at a time such that the exactlycorrect mass of air is drawn into the cylinder), the pressure willdecrease during expansion phase and be equal to the target pressureapproximately at BDC. If the valve is closed too early, the chamber willreach target pressure before BDC and will have expanded less air duringthe stroke than it could have (i.e., there will be a loss of capacity).If the high-side valve is closed too late, then the chamber pressurewill still be above target at BDC, and the pressure difference willentail a loss once the valve is opened.

The last valve transition is at the end of the expansion stroke, whenthe low-side valve is opened. Ideally, the pressure at the end of theexpansion stroke is equal to the target pressure exactly at BDC. If thechamber pressure drops to the target pressure before BDC, then the valveis opened to prevent the crankshaft from having to work to pull thepiston down. If the piston reaches BDC before the pressure has decreasedto the target, then the valve should also open. (An exception may occurif the chamber pressure is above the maximum allowable vent pressure.)This valve opening event is also impacted by the finite valve responsetime, in a manner similar to that described hereinabove for other valveactuation events.

It will be evident to persons familiar with pneumatics and hydraulicdevices that similar considerations apply to the timing and non-idealityof valve actuation events during a compression mode of system 900. Forexample, at the transition between a compression stroke and adirect-fill stroke, as described hereinabove, the high-side valve of acylinder opens. If the high-side valve is opened too late, the pressurewithin the chamber will exceed that within the high-side component(e.g., high-pressure storage vessel), and gas will expand from thechamber into the high-side component in a non-work-performing mannerupon valve actuation. If the high-side valve is opened too soon, thepressure within the chamber will be less than that within the high-sidecomponent, and gas will expand from the high-side component into thechamber in a non-work-performing manner upon valve actuation. Valveactuation timing is similarly constrained at other transitions betweenthe other phases of cylinder operation during a compression process.

FIG. 10 is an illustrative plot of cylinder pressure as a function oftime for four different expansion scenarios in an illustrative CAESsystem similar or even identical to the system 200 shown in FIG. 2.Points A, B, C, D, and E in FIG. 10, marked by dots, correspond tooperating states of one or more components of system 200, or to changesin such operating states, as described below. In the illustrative plotshown, Point A represents an initial state of the pneumatic cylinderassembly (201 in FIG. 2) during which the piston slidably disposedtherein (202 in FIG. 2) is at top dead center and the high-side valve(220 in FIG. 2) between the storage reservoir (222 in FIG. 2) and thelower-pressure cylinder assembly 201 is opened. Point B represents theend of a direct-drive phase of operation during which the high-sidevalve 220 between the storage reservoir 222 and the lower-pressurecylinder assembly 201 is closed and the pressure inside the cylinderassembly 201 is approximately equal to the bottle pressure P_(b) (i.e.,the pressure of gas inside storage reservoir 222 in FIG. 2 (e.g., 300psi)). Point C represents the end of an expansion stage or phase, duringwhich the quantity of gas admitted into the cylinder assembly 201performs work on the piston 202 slidably disposed therein, from top deadcenter at a bottle pressure P_(b) to bottom dead center at an exhaustpressure P_(exhaust). Point C also represents the opening actuation ofthe low-side valve (221 in FIG. 2) between the vent to atmosphere (223in FIG. 2) and the cylinder assembly 201 when the piston 202 is atbottom dead center. Points A, B, and C represent approximately the sameoperating states in all four scenarios of operation of system 200described hereinbelow.

Four versions of Point D (labeled D₁, D₂, D₃, and D₄ to correspond tothe four different valve-actuation scenarios) represent the end of theexhaust stage and beginning of a pre-compression stage; event D thuscorresponds to the closing actuation of the low-side valve 221 betweenthe vent 223 (or a lower-pressure stage) and the cylinder assembly 201.Four versions of event E (E₁, E₂, E₃, and E₄ for the four differentvalve-actuation scenarios) represent the end of the pre-compressionstage, at which time the piston 202 is again at top dead center and thepressure inside the cylinder assembly 201 is approximately equal to thebottle pressure P_(b). If the system is operated cyclically, Point E(any version) immediately precedes Point A and the expansion cycle maybe repeated. The pressure inside the cylinder assembly 201 at the end ofthe pre-compression stroke (i.e., at any version of Point E) isdetermined by the relative timing of the closing of the low-side valve221 (i.e., at any version of Point D).

In an idealized expansion scenario (Scenario 1, represented by a solidline in FIG. 10), there is no dead volume in the cylinder assembly 201and all valve actuations occur instantaneously. The low-side valve 221closes at Point D₁ when the piston 202 is at top dead center,instantaneously followed by the opening of the high-side valve 220 atPoint E₁. In Scenario 1, pressurization of the cylinder assembly 201occurs immediately and with no coupling loss, as there is no volume topressurize at the top of stroke: this instantaneous pressurization ofcylinder assembly 201, simultaneous with D₁ and E₁, is represented bythe perfect verticality of the Scenario 1 line in FIG. 10 at PointD₁/E₁. Scenario 1 is shown as a reference line in FIG. 10.

In a second scenario (Scenario 2, represented by a bold dashed line inFIG. 10), dead volume exists in the cylinder assembly 201. Between PointC and Point D₁, the piston 202 performs a return stroke within thecylinder assembly 201, with the low-side valve 221 open to allow ventingof gas from the upper chamber of cylinder assembly 201. At Point D₁, thelow-side valve 221 is closed so that the gas remaining in the upperchamber of cylinder assembly 201 will be pressurized during theremainder of the return stroke. However, in Scenario 2 the low-sidevalve 221 is closed too late, trapping an insufficient amount of gas inthe upper chamber of cylinder assembly 201, so when the piston 202reaches top dead center the gas inside the upper chamber of cylinderassembly 201 is at a pressure P₂ that is lower than the storage bottlepressure P_(b). In other words, operational Point D₂ occurs too late intime (or piston position) to allow adequate pre-compression by Point E₂of the gas remaining in the cylinder assembly 201. Adequatepre-compression would be to approximately reservoir pressure P_(b). Whenthe high-side valve is opened at Point E₂, a coupling loss occurs whenpressurized gas at reservoir pressure P_(b) is admitted from the storagereservoir 222 (or, in some other embodiments, the previous cylinderstage) to the lower-pressure cylinder assembly 201.

In a third scenario (Scenario 3, represented by a short-dash line inFIG. 10), point D₃, i.e., closure of the valve 221 between the vent 223and the cylinder assembly 201, is timed correctly to enable the gas inthe upper chamber of cylinder assembly 201 to reach a pressure P₃ whenthe piston 202 is at top dead center (point E₃), where P₃ substantiallyequal to the stored bottle pressure P_(b). In other words, operationalPoint D₃ is at the correct time (or piston position) so thatpre-compression of the gas remaining in the cylinder assembly 201 is toa pressure P₃ approximately equal to the reservoir pressure P_(b) atPoint E₃. When the pressure P₃ inside the upper chamber of the cylinderassembly 202 is approximately equal to the pressure P_(b) of gas fromthe storage reservoir 222 (or previous cylinder stage), then there willbe little or no coupling loss when valve 220 is opened, and overallsystem efficiency and performance will be improved.

In a fourth scenario (Scenario 4, represented by a bold dotted line inFIG. 10), the valve 221 between the vent 223 and the cylinder assembly201 is closed (point D₄) too soon and the pressure inside the upperchamber of cylinder assembly 201 reaches a pressure P₄ higher than thestored bottle pressure P_(b) when the piston 202 reaches top dead center(Point E₄). In other words, operational Point D₄ is too early in time(or piston position) and the pre-compression of the remaining air in theupper chamber of the cylinder assembly 201 exceeds reservoir pressureP_(b) at Point E₄. When the valve 220 between the storage vessel 222 (orearlier cylinder stage) and the cylinder assembly 201 is opened (PointE₄), the difference in pressure between results in a coupling loss.

The system controller (226 in FIG. 2) may be programmed in such a manneras to receive feedback (e.g., information from measurements) fromprevious expansion cycles and the present state of system 200. Suchfeedback, whether informational or mechanical, may be used to adjust thetiming of Point D, the closing of the low-side valve 221 to commencepre-compression. For example, a lookup table may be employed to setvalve actuation times in response to measurements of conditions in thesystem. In one embodiment, the controller 226 utilizes timinginformation from previous expansion strokes and pressure measurements ofthe cylinder 201 and reservoir 222 at the completion of thepre-compression process (Point E) to set the next time of closure ofvalve 221. Such feedback may provide optimal performance of theexpander/compressor, improving efficiency, performance, and systemcomponent lifetime. The time of opening of valve 220 and other events inthe expansion cycle may also be adjusted by the system controller 226based on feedback.

Thus, in accordance with embodiments of the invention, efficiency ismaximized during a gas compression or expansion by a combination offeedforward and feedback control of the valve timing where either earlyor late actuation of the valves would reduce overall efficiency of thecompression or expansion process. This efficiency of the valve timingmay be calculated mathematically by comparing the work required withideal valve timing to the actual measured work with the experimental orsub-optimal valve timing. Other factors that are measurable or may becalculated via measurable values and impact efficiency are the rate ofpressure decrease of the storage system during the expansion process,the rate of mass storage during the compression process, and the degreeof under- or over-pressurization during either process. For both thecompression and expansion processes, there is typically a known idealpressure profile that may be approached by optimizing valve timing. Theideal pressure profile may be approached by determining valve timingthat minimizes or maximizes the integrated work about key points in thepressure-volume curve. Deriving and subjecting the system to such timingvalues constitutes the feedforward component of the valve timingcontroller. Correcting for modeling uncertainties, system disturbances,quickly occurring system changes, or longer-term system drift isperformed by incorporating representative measurements in the valvetiming controller, and this constitutes the feedback component of thevalve timing controller. Each valve transition event may be optimizedfor efficiency as described herein. For example, in opening a high-sidevalve at the end of a compression stroke to begin direct fill, an earlyactuation would cause gas to travel backwards from the high-sidereservoir into the cylinder, reducing efficiency of the compressionprocess, and late actuation would result in a pressure spike, increasingwork required to complete the compression and causing a loss of usefulenergy when the valve opens and the air in the cylinder pressureequalizes with storage. Thus, in short, as utilized herein, “maximizingefficiency” of a compression or expansion process entails valve-timingoptimization to minimize or eliminate lost work during an expansion of aparticular amount of gas or minimizing or eliminating additional workrequired to compress a particular amount of gas.

FIG. 11 is a graphical display of experimental test data from anexpansion process involving expansion of gas first in a high-pressurepneumatic cylinder and then in a low-pressure pneumatic cylinder. Thatis, in the physical system from which the data in FIG. 11 were drawn, afirst, high-pressure cylinder expanded gas from a high pressure P_(H) toan intermediate pressure P_(I) while a second, low-pressure cylindereither (a) did not pre-compress the gas in its expansion chamber from apreexisting default pressure P_(L) (PLOT A in FIG. 11) or (b)pre-compressed the gas in its expansion chamber from the preexistingdefault pressure P_(L) to the intermediate pressure P_(I) (PLOT B inFIG. 12).

In PLOT A, the pressure in the expansion chamber of the first,high-pressure cylinder as a function of time during expansion of thechamber's contents from P_(H) to P_(I) is indicated by curves 1100 and1104, and the pressure in the expansion chamber of the second,low-pressure cylinder as a function of time is indicated by curves 1102,1106, and 1108. Expansion of the gas in the high-pressure cylinder isindicated by curve 1100. The approximately constant pressure of the gasin the low-pressure cylinder, being exhausted by a return strokeconcurrently with the expansion recorded by curve 1100, is indicated bycurve 1102.

At the moment corresponding to labeled point A₁, a valve is opened toplace the expansion chamber of the first, high-pressure cylinder influid communication with the expansion chamber of the second,low-pressure cylinder. Because the two chambers are at differentpressures at that time (i.e., the gas in the high-pressure cylinderchamber is at P₁ and the gas in the low-pressure cylinder chamber is atP_(L)), after point A₁ (valve opening) the pressure within the chamberof the high-pressure cylinder decreases rapidly to an intermediatepressure P_(I2) (curve 1104) while the pressure within the chamber ofthe low-pressure cylinder increases rapidly to the intermediate pressureP_(I2) (curve 1106). By point A₂, shortly after A₁, the pressures in thetwo cylinder chambers have equilibrated. The rapid expansion indicatedby curve 1104 performs no work on any mechanical component of the systemand therefore entails a loss of available energy (i.e., a dead-volumeloss). At point A₂, an expansion occurs in the expansion chamber of thelow-pressure cylinder, from P_(I2) to some low end pressure P_(E1)(curve 1108).

In PLOT B, the pressure in the expansion chamber of the first,high-pressure cylinder as a function of time during expansion of thechamber's contents from P_(H) to I₂ is indicated by curve 1110, and thepressure in the expansion chamber of the second, low-pressure cylinderas a function of time during pre-compression of the gas in thelow-pressure cylinder chamber from P_(L) to approximately P_(I) isindicated by curve 1112. Prior to labeled point B, the low-pressurecylinder is performing an exhaust stroke, and gas is being expelled fromthe expansion chamber of the low-pressure chamber at approximatelyconstant pressure P_(L) through an open exhaust valve. At the momentcorresponding to point B, the valve permitting gas to exit the expansionchamber of the low-pressure cylinder is closed, trapping a fixedquantity of gas within the chamber at pressure P_(L). This quantity ofgas is then compressed to pressure P_(I) as indicated by curve 1112.

At point C, the pressure in the expansion chamber of the low-pressurecylinder is approximately equal to the pressure P_(I) in the expansionchamber of the high-pressure cylinder and a valve is opened to place thetwo chambers in fluid communication with each other. Because the twochambers are at approximately equal pressures, there is no significantequilibration upon valve opening (i.e., there is no curve in PLOT Bcorresponding to the expansion of gas in the high-pressure cylinderindicated by curve 1104 in PLOT A) and thus little or no energy loss dueto equilibration. Subsequent to point C, an expansion occurs in theexpansion chamber of the low-pressure cylinder, from P_(I) to some lowend pressure P_(E2) (curve 1114). In FIG. 11, end pressure P_(E2) is notequal to end pressure P_(E1), but this is not a necessary result of thepre-compression process illustrated in FIG. 11 and end pressure P_(E2)may have any of a range of values in accordance with embodiments of thepresent invention.

FIG. 12 is an illustrative plot of the ideal pressure-volume cycle in acylinder operated as either a compressor or expander. FIG. 12 providesexplanatory context for subsequent figures. Instantaneous and perfectlytimed valve actuations are presumed for the system whose behavior isrepresented in FIG. 12. The horizontal axis represents volume(increasing rightward) and the vertical axis represents pressure(increasing upward). In FIG. 12, the volume represented by thehorizontal axis is the volume of the expansion/compression chamber of acylinder assembly that is similar or identical to cylinder 201 in FIG. 2and is being operated as either an expander or compressor. The fourcurves in FIG. 12 (labeled 1, 2, 3, and 4) form a cyclic loop; eachcurve represents one of the four distinct phases of operation describedabove for both compression and expansion. For a cylinder operating as acompressor, Curves 1 through 4 are traversed counterclockwise (e.g., inorder 1, 4, 3, 2), where Curve 1 represents the direct-fill phase; Curve2 represents the compression stroke; Curve 3 represents the intakestroke; and Curve 4 represents the regeneration stroke. For a cylinderoperating as an expander, Curves 1 through 4 are traversed clockwise(e.g., in order 1, 2, 3, 4). Curve 1 represents the direct-fill phase;Curve 2 represents the expansion stroke; Curve 3 represents the exhauststroke; and Curve 4 represents the precompression stroke. Points A, B,C, and D in FIG. 12 represent valve transition events. As each Event (A,B, C, or D) is traversed during cyclic operation of the cylinder, thevalve actuations that occur at each point depend on whether the cylinderis being operated as an expander or compressor. Specifically, if thecylinder is being operated as a compressor, at Event A a high-side valveV1 (220 in FIG. 2) is closed and a low-side valve V2 (221 in FIG. 2)remains closed; at Event D, V1 remains closed and V2 is opened; at EventC, V1 remains closed and V2 is opened; and at Event B, V1 is openedwhile V2 remains closed. If the cylinder is being operated as anexpander, at Event A, V1 is opened and V2 remains closed; at Event B, V1is closed and V2 remains closed; at Event C, V1 remains closed and V2 isopened; at Event D, V1 remains closed and V2 is closed.

As will be made clear by subsequent figures, the effects of finite(non-ideal, nonzero) actuation times for valves V1 and V2 at all valvetransitions in FIG. 12 tend to decrease system capacity and/orefficiency and to alter the shapes of Curves 1, 2, 3, and 4. Also,mistiming of valve transitions in FIG. 12 may decrease system capacityand/or efficiency. An optimal actuation timing exists for each valveactuation event under any given conditions of operation; this optimaltime will, in general, change as the conditions under which the systemis being operated change (e.g., as the pressure in a high-pressure gasstorage reservoir gradually increases or decreases).

FIG. 13 is an illustrative plot of cylinder chamber pressure as afunction of cylinder chamber volume for three different expansionscenarios in an illustrative CAES system similar or even identical tothe system 200 shown in FIG. 2. FIG. 13 shows the effects of early,correctly timed, and tardy closure of valve V2 in the transition (EventD in FIG. 12; not shown in FIG. 13) from intake phase to pre-compressionphase (i.e., from Curve 3 to Curve 4 in FIG. 12). The three scenariosdepicted in a pressure-volume plot in FIG. 13 greatly resemble thescenarios depicted in a pressure-time plot in FIG. 10, as shall beexplained below.

The region of the expander's pressure-volume cycle portrayed in FIG. 13corresponds to Point A in FIG. 12 as defined for an expansion process.(In a non-ideal system, events occurring during a valve transition eventdo not occur without changes of pressure and volume, and so cannot berepresented by a single point in a pressure-volume plot. The instantthat an actuated valve is commanded to transition is one representationof the start of a valve transition.) The dashed curve 1302 representsthe pressure-volume history of the gas within the cylinder chamberduring the latter part of the pre-compression phase (Curve 4 in FIG. 12)for a scenario (the Correct V2(D) Closure scenario) in which closure ofV2 (the low-pressure valve, 221 in FIG. 2) in the transition from ventphase to pre-compression phase occurs at an optimal time. The CorrectV2(D) Closure scenario corresponds to the curve passing through pointsD₂ and E₂ in FIG. 10.

The thick solid curves 1304, 1306 represent the pressure-volume historyof the gas during the latter part of the pre-compression phase for ascenario (the Late V2(D) Closure scenario) in which closure of V2 in thetransition from vent phase to pre-compression phase is tardy. The LateV2(D) Closure scenario corresponds to the curve passing through pointsD₃ and E₃ in FIG. 10. The thin solid curves 1308, 1310 represent thepressure-volume history of the gas during the latter part of thepre-compression phase for a scenario (the Early V2(D) Closure scenario)in which closure of V2 in the transition from vent phase topre-compression phase occurs too early. The Early V2(D) Closure scenariocorresponds to the curve passing through points D₄ and E₄ in FIG. 10.

All curves in FIGS. 13-16 are traversed, in time, in the sense shown bythe arrowheads attached to each curve.

In the systems whose behavior is partly represented by FIGS. 13-16, thegas volume of the high-side component (e.g., high-pressure storagereservoir 222 in FIG. 2) that is connected to the cylinder through V1 ispresumed to be sufficiently large that exchanges of air between thehigh-side component and the cylinder chamber do not substantially changethe pressure P_(H) of the gas within the high-side component.

In the Correct V2(D) Closure Scenario, closure of V2 traps the correctamount of air in the cylinder chamber to produce at TDC a chamberpressure approximately equal to that the pressure P_(H) within thehigh-side component. In FIG. 13, P_(H) is approximately 21.5 megapascals(MPa). At point 1312, when the gas in the chamber approximates pressureP_(H), V1 is opened; since both the gas in the high-side component andthe gas in the chamber are at or near to P_(H), the pressure of the gasin the chamber does not change significantly. Subsequently, gas istransferred during direct-drive phase at approximately constant P_(H)from the high-side component to the chamber as the piston descends inthe cylinder (solid curve 1314). The effects of dead volume during thetransition from pre-compression phase to direct-drive phase areminimized or even nonexistent in the Correct V2(D) Closure Scenario.

In the Late V2(D) Closure Scenario, closure of V2 traps insufficient airin the chamber to produce at TDC a chamber pressure approximately equalto P_(H). Instead, the gas in the chamber achieves some lower pressureP_(H2); in FIG. 13, P_(H2) is approximately 15 MPa. At point 1316, V1opens; since the gas in the high-side component is at a higher pressure(P_(H)) than the gas in the chamber (P_(H2)), gas from the high-sidecomponent rapidly enters the chamber, raising the pressure of the gas inthe chamber while the volume of the chamber does not changesignificantly. This pressure-volume change at near-constant volume isrepresented by curve 1306. Potentially useful pressure energy is lostduring this non-work-performing expansion of gas from the high-pressurecomponent into the chamber, i.e., a dead-volume loss occurs. At the endof curve 1306, the gas in the chamber reaches point 1312, after whichthe Late V2(D) Closure Scenario coincides with the Correct V2(D) ClosureScenario (curve 1314).

In the Early V2(D) Closure Scenario, closure of V2 traps more air in thechamber than is needed to produce at TDC a pressure approximately equalto P_(H). Instead, the gas achieves some higher pressure P_(H3); in FIG.13, P_(H3) is approximately 25 MPa. At point 1318, V1 opens; since thegas in the high-side component is at a lower pressure (P_(H)) than thegas in the chamber (P_(H3)), gas from chamber rapidly enters thehigh-side component, lowering the pressure of the gas in the chamberwhile its volume does not change significantly. This pressure-volumechange at near-constant volume is represented by curve 1310. Potentiallyuseful pressure energy is lost during this non-work-performing expansionof gas from the chamber into the high-pressure component, i.e., adead-volume loss occurs. At the end of curve 1318, the gas in thechamber is at point 1312, after which the Early V2(D) Closure Scenariocoincides with the Correct V2(D) Closure Scenario (curve 1314).

FIGS. 14A-14C are illustrative plots of cylinder chamber pressure as afunction of cylinder chamber volume for two different expansionscenarios in an illustrative CAES system similar or even identical tothe system 200 shown in FIG. 2. The two scenarios depicted in FIGS.14A-14C are the Correct V1(A) Opening Scenario and the Late V1(A)Opening Scenario. The region of the expander's pressure-volume cycleportrayed in FIGS. 14A-14C corresponds to Point A in FIG. 12 as definedfor an expansion process. Valves V1 and V2 are defined as for FIG. 13.FIGS. 14A-14C show the effects of correctly timed and tardy opening ofvalve V1 in the transition from pre-compression phase to direct-drivephase (i.e., from Curve 4 to Curve 1 in FIG. 12). It is presumed that inthe scenarios depicted in FIGS. 14A-14C, the previous valve transition(Event D in FIG. 12) was optimally made. Three separate figures, FIGS.14A-14C, depicting curves 1402, 1404, and 1406 respectively, areemployed to avoid partial obscuration of curve 1402 by curve 1406.

Curve 1402 of FIG. 14A represents the volume-pressure history of bothscenarios until point 1408 is reached. Thereafter, the two scenariosdiverge. In the Correct V1(A) Opening Scenario, V1 is opened at point1408, just as the cylinder reaches TDC. Because pre-compression wasoptimally performed, the pressure in the chamber approximates P_(H) andthere is little or no gas exchange between the chamber and thehigh-pressure component when V1 is opened, and subsequent to point 1408gas is vented during a direct-drive phase at approximately constantP_(H) from the high-side component to the chamber as the piston descendsin the cylinder (curve 1404 in FIG. 14B). In FIGS. 14A-14C, P_(H) isapproximately 1.82 MPa. The effects of dead volume during the transitionfrom pre-compression phase to direct-drive phase are minimal ornonexistent in the Correct V1(A) Opening Scenario.

In the Late V1(A) Opening Scenario, V1 is not opened at point 1408, whenthe piston is at TDC, but remains closed for a time thereafter. As thepiston descends, the pressure-volume state of the gas in the chamberthus begins to retrace curve 1402 in the opposite direction (left-handportion of curve 1406, FIG. 14C): that is, the gas trapped in thechamber simply begins to re-expand. At point 1410 (FIG. 14C), at whichthe gas in the chamber has achieved some pressure P_(H4) significantlylower than P_(H), V1 is opened. Gas then enters the chamber from thehigh-side component, raising the pressure of the gas in the chamber toP_(H) while the volume of the chamber is increasing (rising portion ofcurve 1406). Potential energy is lost and less work is done during thisnon-work-performing expansion of gas from the high-pressure componentinto the chamber, i.e., a dead-volume loss occurs.

FIG. 15 is an illustrative plot of cylinder chamber pressure as afunction of cylinder chamber volume for three different compressionscenarios in an illustrative CAES system similar or even identical tothe system 200 shown in FIG. 2. FIG. 15 shows the effects of early,correctly timed, and tardy opening of valve V1 in the transition (EventB in FIG. 12, defined for compression mode) from compression phase todirect-fill phase (i.e., from Curve 2 to Curve 1 in FIG. 12). The regionof the expander's pressure-volume cycle portrayed in FIG. 15 correspondsto Point B in FIG. 12 as defined for a compression process.

The dotted curve 1502 (partly obscured by thick solid curve 1504)represents the pressure-volume history of the gas within the cylinderchamber during the latter part of the compression phase (Curve 2 in FIG.12) for a scenario (the Correct V1(B) Opening scenario) in which openingof V1 in the transition from compression phase to direct-fill phaseoccurs at an optimal time. The thick solid curve 1504 represents thepressure-volume history of the gas in the chamber during the latter partof the compression phase for a scenario (the Late V1(B) Openingscenario) in which opening of V1 in the transition from compressionphase to direct-fill phase is tardy. The thin solid curve 1506represents the pressure-volume history of the gas during the latter partof the compression phase for a scenario (the Early V1(B) Openingscenario) in which opening of V1 in the transition from compressionphase to direct-fill phase occurs too early.

In the system whose behavior is partially depicted in FIG. 15, V1 and V2have nonzero actuation times. Therefore, the optimal time of opening ofV1 (i.e., the timing of V1 opening for the Correct V1(B) Openingscenario) occurs at point 1508, before the pressure in the chamberreaches P_(H). At point 1508 the gas in the cylinder chamber has not yetachieved the pressure P_(H) of the gas in the high-pressure component,but only a small amount of gas is throttled through the partly-openvalve into the chamber as the pressure-volume state of the gas in thechamber evolves from point 1508 to point 1510, at which time thepressure in the chamber approximates P_(H). A small amount of pressureovershoot may occur (represented by the small hump in curve 1502);subsequently, gas is exhausted during direct-fill phase at approximatelyconstant P_(H) from the cylinder chamber to the high-side component asthe piston continues to ascend in the cylinder (curve 1512). The effectsof dead volume during the transition from pre-compression phase todirect-drive phase are minimal or nonexistent in the Correct V1(B)Opening Scenario.

In the Late V1(B) Opening scenario, V1 is opened at point 1514, by whichtime the gas in the chamber has reached a pressure P_(H5), significantlyhigher than P_(H). After the tardy opening of V1, gas in the chambertransfers into the high-pressure component as the pressure in thechamber decreases (left-hand side of large hump in curve 1514). Energyis lost during this non-work-performing expansion of gas from thechamber into the high-pressure component, i.e., a dead-volume lossoccurs.

A similar curve would be traced even if the valve started to transitionopen at point 1510 when the pressures are equal, due to the nonzero timeto open the valve and pressure rise that occurs with a partially openvalve. Notably, in systems employing a pressure-driven check valve forV1 rather than an actuated valve, a pressure-volume history similar tothat of the Late V1(B) Opening scenario (curve 1504), although notnecessarily so extreme, typically occurs in every compression cycle, asan overpressure (e.g., P_(H5) or some other pressure significantlyhigher than P_(H)) must be achieved on the chamber side of V1 withrespect to the high-pressure-component side of V1 in order for V1 to beactuated. The use of actuated valves rather than check valves in CAESsystems is thus advantageous in this, as well as in other, respects.

In the Early V1(B) Opening scenario, V1 is opened at point 1516, bywhich time the gas in the chamber has reached a pressure of only P_(H6),significantly lower than P_(H). After the early opening of V1, gas inthe high-pressure component flows into the chamber as the pressure inthe chamber increases (right-hand side of curve 1506). Energy is lostduring this non-work-performing expansion of gas from the high-pressurecomponent into the chamber, i.e., a dead-volume loss occurs.

FIG. 16 is an illustrative plot of cylinder pressure as a function ofcylinder volume for three different compression scenarios in anillustrative CAES system similar or even identical to the system 200shown in FIG. 2. FIG. 16 shows the effects of early, correctly timed,and tardy opening of valve V2 in the transition (Event D in FIG. 12,defined for compression mode) from regeneration phase to intake phase(i.e., from Curve 4 to Curve 3 in FIG. 12). The region of the expander'spressure-volume cycle portrayed in FIG. 16 corresponds to Point D inFIG. 12 as defined for a compression process.

The dotted curve 1602 represents the pressure-volume history of the gaswithin the cylinder chamber during the latter part of the regenerationphase (Curve 4 in FIG. 12) for a scenario (the Correct V2(D) Openingscenario) in which opening of V2 in the transition from regenerationphase to intake phase occurs at an optimal time. The thick solid curve1604 represents the pressure-volume history of the gas in the chamberduring the latter part of the compression phase for a scenario (the LateV2(D) Opening scenario) in which opening of V2 in the transition fromregeneration phase to intake phase is tardy. The thin solid curve 1606represents the pressure-volume history of the gas during the latter partof the compression phase for a scenario (the Early V2(D) Openingscenario) in which opening of V2 in the transition from regenerationphase to intake phase occurs too early.

In the system whose behavior is partially depicted in FIG. 16, V1 and V2have nonzero actuation times. Therefore, the optimal time of opening ofV2 (the timing of V2 opening for the Correct V2(D) Opening scenario)occurs at point 1608, before the pressure in the chamber approximatesP_(L) (the pressure of the low-pressure component that communicates withthe cylinder through V2, e.g., vent 223 in FIG. 2). The gas in thecylinder chamber has not yet decreased to the pressure P_(L) of the gasin the low-pressure component, but only a small amount of gas isthrottled through the partly-open valve V2 into the chamber as thepressure-volume state of the gas in the chamber evolves from point 1608to point 1610, at which time the pressure in the chamber approximatesP_(L). A small amount of pressure overshoot may occur (dip in curve1602); subsequently, gas is admitted to the chamber during the intakephase at approximately constant P_(L) from the low-side component to thechamber as the piston continues to descend in the cylinder. The effectsof dead volume during the transition from regeneration phase to intakephase are minimal or nonexistent in the Correct V2(D) Opening Scenario.

In the Late V2(D) Opening scenario, V2 is opened at point 1612, by whichtime the gas in the chamber has decreased to a pressure of P_(L2),significantly lower than P_(L). After the tardy opening of V2, gas fromthe low-pressure component flows into the chamber as the pressure in thechamber increases (right-hand side of large dip in curve 1604). Energyis lost during this non-work-performing expansion of gas into thechamber from the low-pressure component: i.e., a dead-volume lossoccurs.

Notably, in systems employing a pressure-driven check valve for V2rather than an actuated valve, a pressure-volume history similar to thatof the Late V2(D) Opening scenario (curve 1604) typically occurs inevery compression cycle, as an underpressure (e.g., P_(L2) or some otherpressure significantly lower than P_(L)) must be achieved on the chamberside of V2 with respect to the low-pressure-component side of V2 inorder for V2 to be actuated. The use of actuated valves rather thancheck valves in CAES systems is thus advantageous in this, as well as inother, respects.

In the Early V2(D) Opening scenario, V2 is opened at point 1614, bywhich time the gas in the chamber has only declined to a pressure ofP_(L3), significantly higher than P_(L). After the early opening of V2,gas in the chamber exits to the low-pressure component as the pressurein the chamber decreases (left-hand side of curve 1606). Energy is lostduring this non-work-performing expansion of gas from chamber into thelow-pressure component, i.e., a dead-volume loss occurs.

It will be clear to persons familiar with the sciences of hydraulics andpneumatics that considerations similar to those described above withreference to FIGS. 10 and 13-16 also pertain to optimal, early, and latevalve actuation at valve transition events not explicitly depictedherein, for both compression and expansion modes of operation of a CAESsystem. Optimization by the means described of valve actuations at allvalve transition events in a CAES system is contemplated and within thescope of the invention. In brief, wherever two or more volumes of gasare to be brought into fluid communication with each other in the courseof operating a CAES system, optimally timed valve actuations willgenerally be those that occur at moments calculated to bring the volumesof gas into fluid communication with each other when their pressures areapproximately equal.

Generally, the systems described herein may be operated in both anexpansion mode and in the reverse compression mode as part of afull-cycle energy storage system with high efficiency. For example, thesystems may be operated as both compressor and expander, storingelectricity in the form of the potential energy of compressed gas andproducing electricity from the potential energy of compressed gas.Alternatively, the systems may be operated independently as compressorsor expanders.

Embodiments of the invention may, during operation, convert energystored in the form of compressed gas and/or recovered from the expansionof compressed gas into gravitational potential energy, e.g., of a raisedmass, as described in U.S. patent application Ser. No. 13/221,563, filedAug. 30, 2011, the entire disclosure of which is incorporated herein byreference.

The terms and expressions employed herein are used as terms ofdescription and not of limitation, and there is no intention, in the useof such terms and expressions, of excluding any equivalents of thefeatures shown and described or portions thereof, but it is recognizedthat various modifications are possible within the scope of theinvention claimed.

What is claimed is:
 1. A method of increasing efficiency of anenergy-recovery process performed in a cylinder assembly in which gas isexpanded, the cylinder assembly being selectively fluidly connected to ahigh-side component by a high-side valve and selectively fluidlyconnected to a low-side component by a low-side valve, the methodcomprising: performing a first valve transition by opening the high-sidevalve to allow compressed gas to enter the cylinder assembly from thehigh-side component, the cylinder assembly containing gas at a firstpressure prior to the first valve transition; performing a second valvetransition by closing the high-side valve, the gas within the cylinderassembly expanding thereafter; performing a third valve transition byopening the low-side valve to allow a portion of the expanded gas toenter the low-side component from the cylinder assembly, wherein (i) aremnant portion of the gas remains in the cylinder assembly after thethird valve transition and (ii) the expanded gas is at a second pressureprior to the third valve transition; performing a fourth valvetransition by closing the low-side valve, the remnant portion of the gaswithin the cylinder assembly being compressed thereafter toapproximately the first pressure; and enforcing a transition restrictioncomprising at least one of (i) performing the first valve transitiononly when the first pressure is approximately equal to a pressure of thehigh-side component or (ii) performing the third valve transition onlywhen the second pressure is approximately equal to a pressure of thelow-side component.
 2. The method of claim 1, wherein the high-sidecomponent comprises a compressed-gas storage reservoir.
 3. The method ofclaim 1, wherein the high-side component comprises a second cylinderassembly for at least one of compressing gas or expanding gas within apressure range higher than a pressure range of operation of the cylinderassembly.
 4. The method of claim 1, wherein the high-side componentcomprises a mid-pressure vessel for containing gas at a pressure withinboth of or between pressure ranges of operation of the cylinder assemblyand a second cylinder assembly for at least one of compressing gas orexpanding gas within a pressure range higher than a pressure range ofoperation of the cylinder assembly.
 5. The method of claim 1, whereinthe low-side component comprises a vent to atmosphere.
 6. The method ofclaim 1, wherein the low-side component comprises a second cylinderassembly for at least one of compressing gas or expanding gas within apressure range lower than a pressure range of operation of the cylinderassembly.
 7. The method of claim 1, wherein the low-side componentcomprises a mid-pressure vessel for containing gas at a pressure withinboth of or between pressure ranges of operation of the cylinder assemblyand a second cylinder assembly for at least one of compressing gas orexpanding gas within a pressure range lower than a pressure range ofoperation of the cylinder assembly.
 8. The method of claim 1, whereinthe high-side valve and the low-side valve are actuated valves.
 9. Themethod of claim 8, wherein each of the high-side valve and the low-sidevalve is a hydraulically actuated valve, a variable cam actuated valve,an electromagnetically actuated valve, a mechanically actuated valve, ora pneumatically actuated valve.
 10. The method of claim 1, wherein thesecond valve transition is timed to admit an amount of gas into a volumeof the cylinder assembly that is expandable to the second pressuretherein.
 11. The method of claim 1, further comprising monitoring atleast one of a temperature within the cylinder assembly, a pressurewithin the cylinder assembly, a position of a boundary mechanism withinthe cylinder assembly, the pressure of the high-side component, or thepressure of the low-side component during an expansion cycle comprisingthe first, second, third, and fourth valve transitions, therebygenerating control information.
 12. The method of claim 11, furthercomprising utilizing the control information in a subsequent expansioncycle to control timing of at least one of the first, second, third, orfourth valve transitions of the subsequent expansion cycle.
 13. Themethod of claim 12, wherein the timing is controlled to maximizeefficiency of the subsequent expansion cycle.
 14. The method of claim 1,further comprising thermally conditioning gas with heat-transfer fluidduring at least a portion of an expansion cycle comprising the first,second, third, and fourth valve transitions.
 15. The method of claim 14,wherein the thermal conditioning renders the gas expansion substantiallyisothermal.
 16. A method of increasing efficiency of an energy-recoveryprocess performed in a cylinder assembly in which gas is expanded, thecylinder assembly being selectively fluidly connected to a high-sidecomponent by a high-side valve and selectively fluidly connected to alow-side component by a low-side valve, the method comprising:performing, within the cylinder assembly, a plurality of expansioncycles each comprising: performing a first valve transition by openingthe high-side valve to allow compressed gas to enter the cylinderassembly from the high-side component, performing a second valvetransition by closing the high-side valve, the gas within the cylinderassembly expanding thereafter, performing a third valve transition byopening the low-side valve to allow a portion of the expanded gas toenter the low-side component from the cylinder assembly, a remnantportion of the gas remaining in the cylinder assembly after the thirdvalve transition, and performing a fourth valve transition by closingthe low-side valve, the remnant portion of the gas within the cylinderassembly being compressed thereafter; and during each expansion cycle,altering a timing of at least one of the first, second, third, or fourthvalve transitions to maximize efficiency of the expansion cycle.
 17. Themethod of claim 16, wherein the timing is altered based at least in parton control information generated during a previous expansion cycle. 18.The method of claim 17, wherein the control information comprises atleast one of a temperature within the cylinder assembly, a pressurewithin the cylinder assembly, a position of a boundary mechanism withinthe cylinder assembly, the pressure of the high-side component, or thepressure of the low-side component.